Planar optical waveguide element, chromatic dispersion compensator, optical filter, optical resonator and methods for designing the element, chromatic dispersion compensator, optical filter and optical resonator

ABSTRACT

There is provided a planar optical waveguide element including a core, the core including first and second portions and a gap portion that is positioned in a center of a width direction of the core between the first and second portions so as to extend in a light waveguide direction. The gap portion has a lower refractive index than that of the first and second portions, and a single mode propagated in the waveguide element has a span crossing the first and second portions.

CROSS-REFERENCE TO RELATED APPLICATION

This is a Divisional of application Ser. No. 12/870,684, filed Aug. 27,2010, which priority is claimed on International Application No.PCT/JP2009/053763, filed on Feb. 27, 2009, which claims priority toJapanese Patent Application No. 2008-051346, filed Feb. 29, 2008. Thecontents of the aforementioned applications are incorporated herein byreference.

TECHNICAL FIELD

Apparatuses and embodiments described herein related to a planar opticalwaveguide element and design method thereof, in which the planar opticalwaveguide element can be used in various applications such as awavelength dispersion compensation element, an optical filter and anoptical resonator and the like.

BACKGROUND ART

The following are examples of wavelength dispersion compensation in anoptical waveguide structure which does not consider polarizationdependence.

An element having a plurality of Bragg grating elements in which thecycle changes spatially such that wavelength dispersion is compensatedin a plurality of wavelength channels is disclosed in Patent document 1(U.S. Pat. No. 6,865,319) as a dispersion compensation element which hasa Bragg grating pattern on the waveguide. Moreover, Patent document 1also discloses that a refractive index distribution n (z) of the Bragggrating which is formed by a plurality of elements extending in thedirection of the optical axis of the waveguide also shows sinusoidalchanges as shown in the following formula (wherein z is the position ofa point on the light propagation axis).

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 1} \right\rbrack & \; \\{{n(z)} = {{n_{eff}(z)} + {\sum\limits_{i = 1}^{m}{\Delta\;{n_{i}(z)}{\sin\left( {{\int_{0}^{z}{\frac{2\pi}{p_{i}\left( z^{\prime} \right)}\ {\mathbb{d}z^{\prime}}}} + \phi_{i}} \right)}}}}} & \left( {{Formula}\mspace{14mu} 1} \right)\end{matrix}$

In a sine wave component which corresponds to the Bragg grating patternof each wavelength channel, the pitch (local cycle) p, gradually changes(i.e., chirps) together with z. In FIG. 3 of Patent document 1, thepitch chirps in a direction in which it decreases in response toincreases in z. In addition, an origin phase φ_(i) changes discretely ineach grating element i. As in the above described formula, the Bragggrating pattern which corresponds to each channel is definedindependently, and a Bragg grating pattern is formed by superimposingthese patterns. In Patent document 1, a case is illustrated in which aBragg grating pattern is formed in an optical fiber.

In Patent document 2 (U.S. Pat. No. 6,707,967), a wavelength dispersioncompensation element is described in which a Bragg grating having onecycle is formed on the waveguide path, and a sampling structure isformed on the waveguide path which is superimposed on this Bragggrating, so that wavelength dispersion compensation is performed in aplurality of wavelength channels. The sampling structure is formed by apattern that has undergone phase sampling in one cycle which is longerthan the cycle of the Bragg grating. Each cycle of the phase sampling isdivided into a plurality of spatial areas in a direction along theoptical axis of the waveguide, and the phase of the Bragg gratingchanges discontinuously at a boundary where mutually adjacent spatialareas are in contact with each other. As is shown in FIG. 1A throughFIG. 1D of Patent document 2, there are no discontinuous phase changeswithin a single spatial area.

In Patent document 3 (Japanese Patent No. 3262312), a two-input andtwo-output light dispersion equalizer is described that performswavelength dispersion compensation. The light dispersion equalizer has astructure as a basic component element in which two optical waveguidesare coupled by a plurality of directional couplers, the optical pathlengths of two waveguides in a region sandwiched by two adjacentdirectional couplers are mutually different, and a phase controller isprovided in at least one of the two waveguides. In this document, adevice is illustrated that compensates a dispersion slope using thesewaveguides, and an element that compensates wavelength dispersion isprovided in an optical input section. Furthermore, this document alsodescribed that increasing the number of stages formed by connecting theaforementioned basic component elements in series, in order to increasethe compensation effect.

In Patent document 4 (Japanese Patent No. 3415267), a design method foran optical signal processor is described in which a structure providedwith a directional coupler having an amplitude coupling ratio rangingfrom a positive value to a negative value on one side of two waveguideshaving an optical path difference is used as a basic component element,and these basic component elements are combined in a series so as toform a two-input and two-output optical circuit with no feedback(namely, no reflection). In this design technique, the structure of theoptical circuit is decided by expressing the characteristics of theoptical circuit using a two-row two-column unitary matrix, imparting thedesired output characteristics of the cross-port, and calculatingamplitude parameters of the directional coupler in which the amplitudeparameters are unknown parameters of the optical circuit. An example ofthe design of a wavelength dispersion compensation element that is basedon this design method is given in the Examples.

In Patent document 5 (Japanese Patent No. 3917170), a broadbandwavelength dispersion compensation element that employs a highrefractive index waveguide that uses photonic crystals is described, andin which wavelength dispersion compensation is performed by atransmission type of optical waveguide structure. The coding of thewavelength dispersion can be changed.

In Non-patent document 1 (“Phase-Only Sampled Fiber Bragg Gratings forHigh-Channel-Count Chromatic Dispersion Compensation” H. Li, Y. Sheng,Y. Li and J. E. Rothenberg, Journal of Lightwave Technology, Vol. 21,No. 9, September 2003, pp. 2074-2083), an actual fiber Bragg gratingwavelength dispersion compensation element is prepared using a designtechnique similar to that of Patent document 2, and the result of thisis described. Firstly, a Bragg grating pattern of a single channel in acenter wavelength is designed using the information in Non-patentdocument 2 (“An Efficient Inverse Scattering Algorithm for the Design ofNonuniform Fiber Bragg Gratings” R. Feced, M. N. Zervas and M. A.Muriel, IEEE Journal of Quantum Electronics, Vol. 35, No. 8, 1999, pp.1105-1115). The grating pattern is derived using an inverse scatteringsolution from the spectrum characteristics of the desired reflection andwavelength dispersion. However, in the fiber Bragg grating, becausethere are limits to the range over which the refractive index can bechanged in order to manufacture a grating pattern, an operation in whichthe aforementioned spectrum characteristics are apodized by undergoingan inverse Fourier transform is also carried out so that these limitsare not exceeded. As a result of this, a pattern is obtained in whichthe pitch of the Bragg grating changes continuously together with theposition. Thereafter, Bragg grating patterns are designed using phasesampling for a plurality of channels. In a fiber Bragg grating, becausethere are limits on the range of refractive index change, phase samplingis effective.

In Non-patent document 2, an algorithm of a solution for the problem ofinverse scattering which is based on layer peeling solution isdescribed, and an example of the analysis of a wavelength dispersioncompensation element that employs a fiber Bragg grating is illustrated.

In Non-patent document 3 (“Integrated-Optic Dispersion Compensator thatuses Chirped Gratings” C. J. Brooks, G. L. Vossler and K. A. Winick,Optics Letters, Vol. 20, No. 4, 1995, pp. 368-370), a wavelengthdispersion compensation element that employs a chirped Bragg gratingwaveguide on a substrate is described. In this wavelength dispersioncompensation element, a rectangular optical waveguide core is formed bysilver ion exchange on a silica glass substrate, and a Bragg gratingpattern is formed in silica cladding on a top portion of the core.Because the grating pitch is gradually changed, the propagation axis ofthe core of the optical waveguide is bent. Laser light pulses having awavelength of 800 nm are irradiated thereon so that 58 ps/nm is obtainedfor an optical waveguide having a 7 mm grating length. Using a gratinghaving a length of 50 mm, it is possible to perform wavelengthdispersion compensation for an optical fiber equivalent to 50 km at awavelength of 1550 nm.

In FIGS. 1 (a) and (b) and FIG. 3 (a) of Non-patent document 4 (“Guidingand Confining Light in Void Nanostructure” Vilson R. Almeida et. al,Optics Letters, Vol. 29, No. 11, 2004, pp. 1209-1211), a slot-typeoptical waveguide element is described that has a structure in whichlight is confined in silica glass (having a refractive index of 1.46, awidth of 50 nm and a height of 300 nm) in a center gap region that issandwiched between rectangular silicon (i.e., between two locations thateach have a refractive index of 3.48, a width of 180 nm and a height of300 nm).

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

The amount of information that can be transmitted by opticalcommunication has been constantly increasing. In response to this,measures such as (I) increasing the transmission rate of a signal, and(II) increasing the number of channels in wavelength multiplexingcommunication are being promoted.

In optical communication, optical signals are transmitted using lightpulses. Consequently, the following problems occur in the aforementionedmeasure (I). If the transmission rate increases, the time width of thelight pulses is shortened, and the intervals between adjacent lightpulses on a time axis becomes narrower. Because of this, it is crucialfor the temporal waveform of the light pulses to be controlled. On atransmission path formed by an optical fiber, because of wavelengthdispersion in which the propagation rate differs depending on thewavelength of the light, the time width of the light pulses becomesbroader as they travel along the optical fiber. Because of this,technology for wavelength dispersion compensation is required in whichan optical element having the opposite coding wavelength dispersion fromthat of the optical fiber is provided on the optical fiber transmissionpath, and wavelength dispersion is removed from the light pulses afterthey have traveled along the transmission path. The above describedPatent documents 1 to 5 provide technology for a wavelength dispersioncompensation element for measure (I). In particular, in Patent documents1 and 2, technology is described which relates to a multichannelwavelength dispersion compensation element that deals with a pluralityof channels of wavelength multiplexing optical fiber communication.

In contrast, measures (II) have the problems that, because thetransmission path becomes more complex as the number of opticalcomponents increases, they lead to increased size, increased complexity,and increased costs for the optical communication equipment.

In order to avoid increases in the size and complexity of opticalcommunication equipment, it is necessary to miniaturize the componentelements such as the circuits and components of the devices that make upthe optical communication equipment, and to then integrate theminiaturized component elements so as to avoid any increase in thenumber of components. In order to achieve a miniaturization of theoptical components, it is essential to miniaturize the optical elementsthat are the fundamental elements making up the optical components.Optical elements that are used for optical communication are commonlyformed using optical waveguides. Because of this, miniaturization of theoptical waveguide is important to miniaturize the optical components. Inorder to miniaturize the optical waveguide, it is essential to use amaterial having a high refractive index such as silicon (Si) or thelike. This is because, as the wavelength of light in a medium isinversely proportional to the refractive index of that medium,dimensions such as the core width of the optical waveguide becomesmaller as the refractive index becomes higher. The refractive index ofSi is approximately 3.5, which is more than 2.3 times the refractiveindex of silica (SiO₂), which is approximately 1.5. Because thematerials having a high refractive index such as Si and the like can beformed on a flat substrate, coupling of a plurality of opticalwaveguides becomes easier, and this materials are suitable for the taskof integrating a plurality of optical components.

In order to avoid increased costs in optical components, it is importantto reduce the manufacturing costs of the optical elements. If theoptical waveguides are miniaturized, the cost of the raw materialsneeded for each optical element also decreases, and unit costs can bereduced. Because materials having a high refractive index such as Si andthe like can be formed on a flat substrate, a large number of opticalelements can be manufactured on one substrate by using a large areasubstrate, and the manufacturing costs can be reduced even further.

In order to obtain wavelength dispersion elements that are small in sizeand suitable for integration by forming optical waveguides on a flatsubstrate using Si and Si-based high refractive index materials, in thedesign of the optical waveguide, it is necessary for the effectiverefractive index of the optical waveguide in a polarization state whichis parallel to the substrate surface to be equivalent to the effectiverefractive index in a polarization state which is orthogonal to thesubstrate surface. This is because the cross-sectional configuration ofthe core of a high refractive index optical waveguide on the flatsubstrate is different from a circular core cross-section of asemiconductor optical fiber. If the effective refractive index of theoptical waveguide is different due to the polarization, then thewavelength dispersion generated in the optical waveguide is also changedby the polarization. In this case, the performance of the wavelengthdispersion compensation element ends up being affected by thepolarization of the light pulses traveling along the optical fiber.

Solving the above described problems is difficult using related arttechnology. A description will now be given of each element of the abovementioned related art technology.

Technology of Patent Document 1

In the technology described in Patent document 1, as an example ofdevice manufacturing, there is only a description of a case in which aBragg grating that uses an optical fiber is formed. Namely, the mainsubject of this technology is an optical fiber Bragg grating. Thecross-section of an optical fiber is circular, and the opticalcharacteristics thereof do not depend on the polarization direction ofthe propagated light. Accordingly, absolutely no mention is made aboutproviding technology that relates to the design of an optical waveguideintended to reduce polarization dependence. In a design that considerspolarization dependence, the effective refractive index is independentlydefined for each of polarization that is parallel to the substratesurface and polarization that is perpendicular to the substrate surface,and it is necessary to optimize the waveguide structure such that thesetwo effective refractive indices match each other. However, in thisdocument, as is described above formula, only a single effectiverefractive index n (z) is defined irrespective of the polarization.Accordingly, it is not possible for the technology of this document tobe applied to the design of wavelength dispersion compensation elementsthat are formed from high refractive index optical waveguides in whichthe polarization dependence on the substrate has been reduced.

Moreover, the design method of the wavelength dispersion compensationelement according to Patent document 1 follows a procedure in which theparameters in the formula such as the element length and amplitude ofthe effective refractive index is determined such that the wavelengthdispersion characteristics obtained by simulation from that structureapproach predetermined characteristics, while determining the shape ofthe effective refractive index pattern of the Bragg grating by theformula in advance. In this design method, a Bragg grating opticalwaveguide is configured only by superimposing the Bragg grating patternsthat correspond to each wavelength channel. Accordingly, the removal ofinterference between wavelength channels has not performed in thisdesign method, therefore the problem arises that the wavelengthdispersion characteristics are deteriorated by the interference betweenwavelength channels. Furthermore, the procedure of this design method isa reverse flow of a procedure of a design method that specifies theeffective refractive index pattern of a Bragg grating from predeterminedelement dimensions or optical characteristics. In order to achieve aminiaturization of the elements, it is essential for the element lengthto be decided in advance. However, this is not possible in the designmethod of Patent document 1.

Technology of Patent Document 2

Patent document 2 does not mention a design that considers polarizationdependence in the same way as in Patent document 1. Accordingly, it isnot possible for the technology of this document to be applied to thedesign of wavelength dispersion compensation elements that are formedfrom high refractive index optical waveguides in which the polarizationdependence on a substrate has been reduced.

In this document, a principle of designing a grating waveguide basedmainly on phase sampling of the grating is employed. The reason for thisis that, because this document is intended for low refractive indexoptical waveguides such as optical fibers whose refractive index iswithin a range of 1.4 to 1.5, it is restricted by the fact that a rangeof what the effective refractive index of the optical waveguide can bechanged is narrow. Patent document 2 mentions that the technology canalso be applied to waveguides on a substrate. However, the technology ofPatent document 2 is suitable only for the same type of low refractiveindex optical waveguides. Accordingly, the technology of Patent document2 is not suitable for the purpose of attaining miniaturization byshortening the grating length as much as possible without reducing thereflectance by widely changing the effective refractive index in areflective optical waveguide.

Furthermore, Patent document 2 discloses that a phase sampling patternis effective in avoiding performance deterioration due to voids when agrating structure is being manufactured. The reason for this is thatthis document is concerned with manufacturing optical fiber gratings,and intended for a manufacturing method in which a grating pattern isprinted on an optical fiber using ultraviolet irradiation. If it wereintended for a high refractive index optical waveguide on a substrate,then it should be expected that there would be no restrictions such asperformance deterioration due to the voids.

Technology of Patent Document 3

Patent document 3 does not mention any technology to reduce polarizationdependence. In the simple optical waveguide structure of this document,it is only possible to compensate a dispersion slope, and it is notpossible to compensate wavelength dispersion. In order to compensatewavelength dispersion, it is necessary to form a structure in whichanother optical element is connected to the optical waveguide. Becauseof this, it is not possible to achieve miniaturization by using thetechnology of this document.

Technology of Patent Document 4

Patent document 4 does not mention any technology to reduce polarizationdependence. In the wavelength dispersion compensation element of thisdocument, because the phase characteristics are anti-symmetrical to thepoint of origin, the wavelength dispersions in adjacent spectrum regionsend up being inverted. Accordingly, this wavelength dispersioncompensation element can only be used for wavelength dispersioncompensation that targets a particular limited spectrum region, namely,that targets specific spectrum region channels. This wavelengthdispersion compensation element cannot be used to compensate wavelengthdispersion in a plurality of channels for the purpose of application towavelength multiplexing optical fiber communication.

Technology of Patent Document 5

The technology of Patent document 5 can compensate wavelength dispersionin a broad wavelength band. However, the technology of Patent document 5cannot deal with multichannel wavelength dispersion. Because of this,the wavelength dispersion value thereof is not large. Accordingly, thistechnology cannot be used to compensate wavelength dispersion in a longdistance (e.g., 40 km) optical fiber transmission path for the purposeof application to wavelength multiplexing optical fiber communication.

Technology of Non-Patent Document 1

The technology of Non-patent document 1 has the same problems as thoseof Patent document 2.

Technology of Non-Patent Document 3

Although this is a Bragg grating optical waveguide formed on a flatsubstrate, a grating pattern is only formed in the cladding region ontop of the optical waveguide core. Accordingly, the effective refractiveindices of the respective optical waveguides are different for linearlypolarized light in a direction parallel to the substrate surface and ina direction perpendicular to the substrate surface. Because of this, thewavelength dispersion performance differs greatly due to thepolarization state. Experiments described in this document wereperformed using a Ti: sapphire laser as a light source. A Ti: sapphirelaser normally emits linearly polarized light. In this document, thereis no description of polarization states, and no consideration is givenas to how to solve the problem of effective refractive index differencesthat are caused by disparities in polarization. Accordingly, it is notpossible for the technology of this document to be applied to the designof wavelength dispersion compensation elements that are formed by highrefractive index optical waveguides in which the polarization dependenceon a substrate has been reduced.

Technology of Non-Patent Document 4

The technology of Non-patent document 4 is characterized in having aspecial structure in which a low refractive index center gap issandwiched in rectangular silicon, and propagated light is confined inthis low refractive index region by narrowing this center gap. The lightpropagation principle itself differs greatly from a typical opticalwaveguide in which propagated light is mainly confined in a highrefractive index region. In optical waveguides that correspond to thisstructure, the machining accuracy of the slot side walls has a largeeffect on the scattering rather than that of the core rib side walls.Moreover, because wave-guided light is distributed more in the lowrefractive index portion than the high refractive index portion, thisstructure is not suited to the purpose of making the opticalcharacteristics variable by making the refractive index of the highrefractive index portions variable.

When the optical waveguide structure shown in FIG. 3 is calculated usinga mode solver, it was found that the light confinement coefficient intwo silicon regions was 42.7%, while in contrast to this, the lightconfinement coefficient in the center gap region which had a surfacearea having a width of 50 nm and a height of 300 nm was 48.0%, so thatthe propagated light was mainly confined in the center gap (i.e., slot)region.

The exemplary embodiments described herein were conceived in view of theabove described circumstances and it is an exemplary object thereof toprovide a planar optical waveguide element, a wavelength dispersioncompensation element using this planar optical waveguide element, and adesign method thereof, in which the planar optical waveguide element canreduce the effects caused by a roughness of the core-side wall which isinevitably generated in a manufacturing process.

Means for Solving the Problem

In order to solve the above described problems, exemplary embodimentsinclude the following.

Namely,

(1) An aspect of an exemplary embodiment is related to a planar opticalwaveguide element wherein an optical waveguide comprises: a core, and agap portion that is positioned in a center of a width direction of thecore so as to extend in a light waveguide direction, and that has alower refractive index than that of the core; and wherein the corecomprises two areas that are separated by the gap portion, and a singlemode optical waveguide, in which a single mode is propagated spancrossing these two areas, is formed.

(2) In the planar optical waveguide element according to (1), it ispreferable that a first Bragg grating pattern and a second Bragg gratingpattern may be respectively formed in areas which are mutually parallelin the light waveguide direction when viewed in a cross-section which isperpendicular to the light waveguide direction; and the first Bragggrating pattern comprises recessed and protruding portions that areformed on both outer side walls of the core of the optical waveguidealong the light waveguide direction; and the second Bragg gratingpattern comprises recessed and protruding portions that are formed,along the light waveguide direction, on both inner side walls of agroove that is formed on a top portion of the core at the center of thewidth direction of the core; and, when viewed in the light waveguidedirection, for portions of the first Bragg grating pattern where a corewidth is wide correspond with portions of the second Bragg gratingpattern where a groove width is narrow, and for portions of the firstBragg grating pattern where the core width is narrow also correspondwith portions of the second Bragg grating pattern where the groove widthis wide.

(3) In the planar optical waveguide element according to (1) or (2), theBragg grating patterns may comprise a plurality of isolated singlecoordinate points where a coding of a gradient of an envelope curve ofan amplitude of a Bragg grating is inverted.

(4) In the planar optical waveguide element according to (1) to (3),that the optical waveguide may comprise a Bragg grating pattern; theBragg grating pattern only uses discrete values of three or moredifferent pitches; these discrete values are each present in a pluralityof locations over an entire length of the optical waveguide; and, if avalue which has the highest distribution frequency among all of thesediscrete values is taken as M, and if a closest value to the M which islarger than the M is taken as A, and if a closest value to the M whichis smaller than the M is taken as B, then a difference expressed as A-Mis equal to a difference expressed as M-B.

(5) In the planar optical waveguide element according to (1) to (4), thecore of the optical waveguide may comprise an inner side core having aprojection which forms a rib structure, and an outer side core which isprovided on top of the inner side core and covers a circumferentialsurface of the projection; and a refractive index of the outer side coremay be lower than an average refractive index of the inner side core.

(6) Moreover, another aspect of an exemplary embodiment is related to awavelength dispersion compensation element which comprises the planaroptical waveguide element according to (1) to (5), and which comprises aBragg grating pattern in an optical waveguide; and in which a wavelengthdispersion and a dispersion slope in the optical waveguide arecompensated by differing a distance over which signal light ispropagated in the optical waveguide between entering the opticalwaveguide and being reflected in accordance with the wavelength, in aplurality of wavelength channels.

(7) Moreover, another aspect of an exemplary embodiment is related to adesign method for the wavelength dispersion compensation elementaccording to (6), wherein the optical waveguide comprises a first Bragggrating pattern and a second Bragg grating pattern each formed in areaswhich are mutually parallel in a light waveguide direction when viewedin a cross-section which is perpendicular to the light waveguidedirection; and wherein the design method comprises: an optical waveguidecross-sectional structure design process in which, by changingdimensions, in a cross-section which is perpendicular to the lightwaveguide direction, of the two areas which form the first Bragg gratingpattern and the second Bragg grating pattern, and thus equalizingeffective refractive indices of the optical waveguide for two mutuallyindependent polarizations that are guided on the optical waveguide, andby then determining a common effective refractive index for the twopolarizations, a relationship between the dimensions of the two areasand the common effective refractive index is obtained; a Bragg gratingpattern design process in which, after a predetermined complexreflectance spectrum is calculated by specifying a wavelengthdispersion, a dispersion slope, and a reflectance as parameters, a shapedistribution of an effective refractive index along the light waveguidedirection is obtained for the optical waveguide from the complexreflectance spectrum and a desired optical waveguide length; and awavelength dispersion compensation element design process in which, byconverting the shape distribution of the effective refractive indexobtained in the Bragg grating pattern design process into a shapedistribution of the dimensions of the two areas based on therelationship between the dimensions of the two areas and the commoneffective refractive index obtained in the optical waveguidecross-sectional structure design process, the first Bragg gratingpattern and the second Bragg grating pattern which are formed by thechanges in the dimensions of the two areas are obtained.

(8) In the design method for the wavelength dispersion compensationelement according to (7), the Bragg grating pattern design processfurther comprises a coarse graining process in which a discretizedresolution of a coordinate axis is taken as more than an amount ofchange in a pitch which corresponds to a half value of a width of areflection band, in other words, more than a maximum value of the amountof change from a center value of the pitch in a chirped Bragg grating;and the optical waveguide is created by the coarse graining process,which includes a plurality of isolated single coordinate points where acoding of a gradient of an envelope curve of an amplitude of a Bragggrating is inverted.

(9) Moreover, another aspect of an exemplary embodiment is related to anoptical filter that comprises the planar optical waveguide elementdescribed in any one of the above (1) through (5).

(10) Moreover, another aspect of an exemplary embodiment is related to adesign method for the optical filter according to (9), wherein theoptical waveguide comprises a first Bragg grating pattern and a secondBragg grating pattern which are mutually parallel in the light waveguidedirection when viewed in a cross-section which is perpendicular to thelight waveguide direction; and wherein the design method comprises: anoptical waveguide cross-sectional structure design process in which, bychanging dimensions, in a cross-section which is perpendicular to thelight waveguide direction, of two areas which form the first Bragggrating pattern and the second Bragg grating pattern, and thusequalizing effective refractive indices of the optical waveguide for twomutually independent polarizations that are guided on the opticalwaveguide, and by then determining a common effective refractive indexfor the two polarizations, a relationship between the dimensions of thetwo areas and the common effective refractive index is established; aBragg grating pattern design process in which, after a predeterminedcomplex reflectance spectrum is calculated by specifying both areflectance and a phase as parameters, a shape distribution of aneffective refractive index along the waveguide direction of the opticalwaveguide is obtained from the complex reflectance spectrum and adesired optical waveguide length; and an optical filter design processin which, by converting the shape distribution of the effectiverefractive index obtained in the Bragg grating pattern design processinto a shape distribution of the dimensions of the two areas based onthe relationship between the dimensions of the two areas and the commoneffective refractive index obtained in the optical waveguidecross-sectional structure design process, the two Bragg grating patternswhich are formed by the changes in the dimensions of the two areas areobtained.

(11) In the design method for the optical filter according to (10), theBragg grating pattern design process may comprise a coarse grainingprocess in which a discretized resolution of a coordinate axis is takenas more than an amount of change in a pitch which corresponds to a halfvalue of a width of a reflection band, in other words, more than amaximum value of the amount of change from a center value of the pitchin a chirped Bragg grating; and the optical waveguide is created by thecoarse graining process, which includes a plurality of isolated singlecoordinate points where a coding of a gradient of an envelope curve ofan amplitude of a Bragg grating is inverted.

(12) Moreover, another aspect of an exemplary embodiment is related toan optical resonator which comprise a first optical waveguide whichforms a first reflection mirror, a second optical waveguide which formsa second reflection mirror, and a third optical waveguide which issandwiched between the first optical waveguide and the second opticalwaveguide; wherein the first optical waveguide, the third opticalwaveguide, and the second optical waveguide are connected in series, sothat a single planar optical waveguide is formed, and wherein the firstoptical waveguide and the second optical waveguide comprises the planaroptical waveguide element according to any one of the above (1) through(5).

(13) Moreover, another aspect of an exemplary embodiment is related to adesign method for the optical resonator according to (12), wherein theoptical waveguide of each of the reflection mirrors comprises a firstBragg grating pattern and a second Bragg grating pattern which aremutually parallel in a light waveguide direction when viewed in across-section which is perpendicular to the light waveguide direction;and wherein the design method comprises: an optical waveguidecross-sectional structure design process in which, by changingdimensions, in a cross-section which is perpendicular to the lightwaveguide direction, of two areas which form the first Bragg gratingpattern and the second Bragg grating pattern, and thus equalizingeffective refractive indices of the optical waveguide for two mutuallyindependent polarizations that are guided on the optical waveguide, andby then determining a common effective refractive index for the twopolarizations, a relationship between the dimensions of the two areasand the common effective refractive index is obtained; a Bragg gratingpattern design process in which, after a predetermined complexreflectance spectrum is calculated by specifying both a reflectance anda phase as parameters, a shape distribution of an effective refractiveindex along the waveguide direction of the optical waveguide is obtainedfrom the complex reflectance spectrum and a desired optical waveguidelength; and a reflection mirror design process in which, by convertingthe shape distribution of the effective refractive index obtained in theBragg grating pattern design process into a shape distribution of thedimensions of the two areas based on the relationship between thedimensions of the two areas and the common effective refractive indexobtained in the optical waveguide cross-sectional structure designprocess, the two Bragg grating patterns which are formed by the changesin the dimensions of the two areas are obtained.

(14) In the design method for the optical resonator according to (13),the Bragg grating pattern design process may further comprise a coarsegraining process in which a discretized resolution of a coordinate axisis taken as more than an amount of change in a pitch which correspondsto a half value of a width of a reflection band, in other words, morethan a maximum value of the amount of change from a center value of thepitch in a chirped Bragg grating; and an optical waveguide is created bythe coarse graining process, which includes a plurality of isolatedsingle coordinate points where a coding of a gradient of an envelopecurve of an amplitude of a Bragg grating is inverted.

Effects of the Invention

According to the exemplary aspect described in (1) above, because themode field diameter of the fundamental mode expands, it is possible toinhibit the effects (i.e., scattering loss) on the opticalcharacteristics from roughness of the core-side walls which are formedfrom a high refractive index material, in which the roughness isunavoidably generated in the manufacturing process.

According to the exemplary aspect described in (2) above, a planaroptical waveguide element having a Bragg grating pattern can reduce thepolarization dependence of the optical characteristics.

According to the exemplary aspect described in (3) above, it is possibleto make the waveguide length shorter than a sampled grating.

According to the exemplary aspect described in (4) above, compared to arelated art chirped grating in which the pitch changes gradually,tolerance control in the manufacturing process is easier and thiscontributes to an improvement in the manufacturing yield.

According to the exemplary aspect described in (5) above, compared to arelated art embedded type of optical waveguide with high relativerefractive index difference which is only formed from two portions,namely, a cladding and a core formed from a high refractive indexmaterial, because the confinement of light in an inner side core whichis formed from a high refractive index material is weaker, it ispossible to inhibit the effects (i.e., scattering loss) on the opticalcharacteristics from roughness of the inner-side of core-side walls, inwhich the roughness is unavoidably generated in the manufacturingprocess.

According to the exemplary aspect described in (6) above, it is possibleto achieve a wavelength dispersion compensation element having littlevariation in the optical characteristics.

According to the exemplary aspect described in (7) above, it is possibleto easily achieve the designing of a wavelength dispersion compensationelement having two types of Bragg grating pattern.

According to the exemplary aspect described in (8) above, it is possibleto design a wavelength dispersion compensation element which isminiaturized even further.

According to the exemplary aspect described in (9) above, it is possibleto achieve an optical filter having little variation in the opticalcharacteristics.

According to the exemplary aspect described in (10) above, it ispossible to easily achieve the designing of an optical filter having twotypes of Bragg grating pattern.

According to the exemplary aspect described in (11) above, it ispossible to design an optical filter which is miniaturized even further.

According to the exemplary aspect described in (12) above, it ispossible to achieve an optical resonator having little variation in theoptical characteristics.

According to the exemplary aspect described in (13) above, it ispossible to easily achieve the designing of an optical resonator havingtwo types of Bragg grating pattern.

According to the exemplary aspect described in (14) above, it ispossible to design an optical resonator which is miniaturized evenfurther.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a cross-sectional view showing a first exemplary embodimentof a planar optical waveguide element.

FIG. 1B is a partial perspective view showing the planar opticalwaveguide element of FIG. 1A.

FIG. 2 is a cross-sectional view showing a second exemplary embodimentof a planar optical waveguide element.

FIG. 3A is a partial plan view showing a grating structure in a planaroptical waveguide element.

FIG. 3B is a cross-sectional view of the grating structure of FIG. 3A.

FIG. 3C is a partial perspective view of the grating structure of FIG.3A.

FIG. 4A is a partial plan view showing another example of a gratingstructure in a planar optical waveguide element.

FIG. 4B is a cross-sectional view of the grating structure of FIG. 4A.

FIG. 4C is a partial perspective view of the grating structure of FIG.4A.

FIG. 5 is a cross-sectional view showing a third exemplary embodiment ofa planar optical waveguide element.

FIG. 6A is a graph showing an example of changes in the effectiverefractive index relative to w_(in).

FIG. 6B is a graph showing an example of changes in w_(out) which areattendant on the change in w_(in).

FIG. 7 is a graph showing the changes in w_(in) and w_(out) relative ton_(eff) in an exemplary embodiment of a planar optical waveguideelement.

FIG. 8 is a graph showing a wavelength dependence of a group delay timedetermined in Example 1 and Reference example 1 of a wavelengthdispersion compensation element.

FIG. 9 is a graph showing an effective refractive index profile inExample 1 of a wavelength dispersion compensation element.

FIG. 10 is a graph showing an enlargement of a portion of the effectiverefractive index profile shown in FIG. 9.

FIG. 11 is a graph showing an enlargement of a portion of the effectiverefractive index profile shown in FIG. 9 together with an envelopecurve.

FIG. 12 is a graph showing a pitch distribution in Example 1 of thewavelength dispersion compensation element.

FIG. 13A is a graph showing the wavelength dependence in the group delaytime obtained in Example 1 of the wavelength dispersion compensationelement.

FIG. 13B is a graph showing an enlargement of the vicinity of a 1571 nmwavelength of FIG. 13A.

FIG. 13C is a graph showing an enlargement of the vicinity of a 1590 nmwavelength of FIG. 13A.

FIG. 13D is a graph showing an enlargement of the vicinity of a 1610 nmwavelength of FIG. 13A.

FIG. 14 is a graph showing an enlargement of a portion of an opticalwaveguide dimensional profile in Example 1 of the wavelength dispersioncompensation element.

FIG. 15 is a cross-sectional view showing a Reference example of aplanar optical waveguide element.

FIG. 16 is a graph showing changes in w_(in) and w_(out) relative ton_(eff) in Reference example 1 of a planar optical waveguide element.

FIG. 17 is a graph showing an effective refractive index profile inReference example 1 of a wavelength dispersion compensation element.

FIG. 18 is a graph showing an enlargement of a portion of an opticalwaveguide dimensional profile in Reference example 1 of a wavelengthdispersion compensation element.

FIG. 19 is a graph showing a wavelength dependence of a group delay timedetermined in Example 2 of a wavelength dispersion compensation element.

FIG. 20 is a graph showing an effective refractive index profile inExample 2 of a wavelength dispersion compensation element.

FIG. 21 is a graph showing a pitch distribution in Example 2 of awavelength dispersion compensation element.

FIG. 22 is a graph showing a wavelength dependence of a group delay timeobtained in Example 2 of a wavelength dispersion compensation element.

FIG. 23 is a graph showing a wavelength dependence of a group delay timedetermined in Example 3 of a wavelength dispersion compensation element.

FIG. 24 is a graph showing an effective refractive index profile inExample 3 of a wavelength dispersion compensation element.

FIG. 25 is a graph showing a pitch distribution in Example 3 of thewavelength dispersion compensation element.

FIG. 26 is a graph showing a wavelength dependence of a group delay timeobtained in Example 3 of a wavelength dispersion compensation element.

FIG. 27 is an explanatory view showing an example of a connection methodfor connecting a wavelength dispersion compensation element and anoptical transmission path.

FIG. 28 is a graph showing optical characteristics specified for Example1 of an optical filter.

FIG. 29 is a graph showing an effective refractive index profile inExample 1 of an optical filter.

FIG. 30 is a graph showing an enlargement of a portion of the effectiverefractive index profile shown in FIG. 29.

FIG. 31 is a graph showing an enlargement of a portion of the opticalwaveguide dimension profile in Example 1 of an optical filter.

FIG. 32 is a graph showing optical characteristics specified for Example2 of an optical filter.

FIG. 33 is a graph showing an effective refractive index profile inExample 2 of an optical filter.

FIG. 34 is a graph showing an enlargement of a portion of the effectiverefractive index profile shown in FIG. 33.

FIG. 35 is a graph showing an enlargement of a portion of the opticalwaveguide dimension profile in Example 2 of an optical filter.

FIG. 36 is a graph showing optical characteristics specified for Example3 of an optical filter.

FIG. 37 is a graph showing an effective refractive index profile inExample 3 of an optical filter.

FIG. 38 is a graph showing an enlargement of a portion of the effectiverefractive index profile shown in FIG. 37.

FIG. 39 is a graph showing an enlargement of a portion of the opticalwaveguide dimension profile in Example 3 of an optical filter.

FIG. 40 is a graph showing optical characteristics specified for Example4 of an optical filter.

FIG. 41 is a graph showing an effective refractive index profile inExample 4 of an optical filter.

FIG. 42 is a graph showing an enlargement of a portion of the effectiverefractive index profile shown in FIG. 41.

FIG. 43 is a graph showing an enlargement of a portion of the opticalwaveguide dimension profile in Example 4 of an optical filter.

FIG. 44 is a typical view showing an example of the structure of anoptical resonator.

FIG. 45 is a graph in which the bottom portion shows reflectionspectrums of both a first and a second reflection mirror, while the topportion shows the product of these two.

FIG. 46 is a graph in which the bottom portion shows intensitycharacteristics of a Fabry-Perot resonance, while the top portion showstransmission characteristics of an optical resonator.

FIG. 47 is a graph in which the top portion shows frequency dependenceof a delay time in an example of an optical element having a singlereflection channel, while the bottom portion shows an absolute value andphase of a complex field reflectance in this example.

FIG. 48 is a contour plan showing simulation results for the lightintensity distribution of a core in Example 1 of the planar opticalwaveguide element shown in FIG. 1A and FIG. 1B.

FIG. 49 is a contour plan showing simulation results for the lightintensity distribution of a core in Example 2 of the planar opticalwaveguide element shown in FIG. 2.

FIG. 50A is a cross-sectional view showing the schematic structure of aplanar optical waveguide element of Comparative example 1.

FIG. 50B is a partial perspective view of this same planar opticalwaveguide element.

FIG. 51 is a cross-sectional view showing the schematic structure of aplanar optical waveguide element of Comparative example 2.

FIG. 52 is a contour plan showing simulation results for the lightintensity distribution of a core in Comparative example 1 of the planaroptical waveguide element shown in FIG. 50A and FIG. 50B.

FIG. 53 is a contour plan showing simulation results for the lightintensity distribution of a core in Comparative example 2 of the planaroptical waveguide element shown in FIG. 51.

DESCRIPTION OF THE REFERENCE NUMERALS

-   -   1, 1A . . . First core region    -   2, 2A . . . Second core region    -   3, 3A . . . Gap portion (Center gap)    -   4, 4A . . . Planar optical waveguide element    -   5, 5A . . . Substrate    -   6, 6A . . . Bottom cladding    -   7, 7A . . . Top cladding    -   10 . . . Core    -   12 . . . Side wall    -   12 a . . . Recessed portion (Narrow portion of core width)    -   12 b . . . Protruding portion (Wide portion of core width)    -   13 . . . Groove    -   13 a . . . Recessed portion (Wide portion of groove width)    -   13 b . . . Protruding portion (Narrow portion of groove width)    -   15 . . . Projection    -   15 a . . . Recessed portion (Narrow portion of projection width)    -   15 b . . . Protruding portion (Wide portion of projection width)    -   20, 30 . . . Planar optical waveguide element    -   21, 31 . . . First rib of inner side core    -   22, 32 . . . Second rib of inner side core    -   23 . . . Center gap    -   24, 34 . . . Outer side core    -   25, 35 . . . Substrate    -   26, 36 . . . Bottom cladding    -   27, 37 . . . Top cladding    -   101 . . . Wavelength dispersion compensation element    -   102 . . . Optical circulator    -   150 . . . Optical resonator    -   151 . . . First optical waveguide (Reflection mirror)    -   152 . . . Second optical waveguide (Reflection mirror)    -   153 . . . Third optical waveguide

BEST MODES FOR CARRYING OUT THE INVENTION

Hereinafter, exemplary embodiments will be described with reference tothe figures.

First Exemplary Embodiment of a Planar Optical Waveguide Element

FIG. 1A and FIG. 1B typically show a first exemplary embodiment of aplanar (substrate type) optical waveguide element. FIG. 1A is across-sectional view, and FIG. 1B is a partial perspective view.

The planar optical waveguide element 4 forms a single mode opticalwaveguide, and the optical waveguide is formed on a substrate 5. Theplanar optical waveguide element includes a gap portion 3 which isprovided in the center of a width direction of the cores 1 and 2 of theoptical waveguide. The gap portion 3 is formed from a material having alower refractive index than that of cores 1 and 2, and extends in thelight waveguide direction. The cores 1 and 2 are separated by the gapportion 3, and a single mode optical guided wave is propagated so as tospan across (straddle) the cores 1 and 2. Specifically, the opticalwaveguide is formed by a bottom cladding 6 which is formed on thesubstrate 5, the cores 1 and 2 that are formed by two L-shaped areaswhich are formed on the bottom cladding 6, the gap portion 3 which isinserted in the center of the cores 1 and 2, and top cladding 7 that isformed on the cores 1 and 2 and on the gap portion 3. The opticalwaveguide of the present embodiment is not limited to being a linearwaveguide, and may also be a curved waveguide.

In this example, the cores 1 and 2 are formed by two areas of a firstrib 1 and a second rib 2. The first rib 1 and second rib 2 are formedfrom a material having a higher refractive index than that of the gapportion 3. The first rib 1 and second rib 2 are the same height, andthis height is indicated by t₂ in FIG. 1A.

The first rib 1 and second rib 2 have an identical shape, and aprotruding portion is formed by the mutually abutting portions of eachone. Specifically, the first rib 1 and second rib 2 include planarportions 1 a and 2 a, and rectangular parallelepiped portions 1 b and 2b which have a height t₁ and which are positioned on edges of the planarportions 1 a and 2 a. The rectangular parallelepiped portions 1 b and 2b form protruding portions having a width w₁. The material used to formthe rectangular parallelepiped portions 1 b and 2 b is the same as thematerial used to form the planar portions 1 a and 2 a. The width of thegap portion 3 is w₂, and the gap portion 3 is formed from a materialhaving a lower refractive index than that of the first rib 1 and secondrib 2.

Examples of the material used to form the first rib 1 and second rib 2include high refractive index materials such as silicon (Si) and thelike. Examples of the material used to form the gap portion 3 includesilica (SiO₂), silicon oxynitride (SiO_(x)N_(y)), silicon nitride(Si_(x)N_(y)), and the like. Materials in which the composition ratiox:y is controlled such that, for example, in SiO_(x)N_(y) the refractiveindex is 1.5, or in Si_(x)N_(y) the refractive index is 2.0, may beused. However, other composition ratios may also be used provided thatthey have a lower refractive index than that of the Si of the ribs 1 and2 which have high refractive index.

P-conductivity or N-conductivity may be imparted to the first rib 1 orthe second rib 2 by doping the medium with suitable impurities. Namely,the first rib 1 may be set as a P-type area, and the second rib 2 may beset as an N-type area. Conversely, the first rib 1 may be set as anN-type area, and the second rib 2 may be set as a P-type area.

The impurities (i.e., dopants) that impart conductivity to the highrefractive index core which is formed by a semiconductor can beappropriately selected in accordance with the maternal medium (basemedium). For example, if the maternal medium is a group-IV semiconductorsuch as silicon, then a group-III element such as boron (B) can be usedas a dopant to impart P-type polarity, and a group-V element such asphosphorus (P) or arsenic (As) can be used as a dopant to impart N-typepolarity.

In this manner, a P-I-N bond is formed in a plane of the core, by makingthe first rib 1 and second rib 2 of the core high refractive index ribswhich are formed from a semiconductor such as Si or the like, and bymaking one of these ribs a P-type and the other one a N-type. Inaddition, by providing an electrode pad that imparts voltage to both thefirst rib 1 and the second rib 2, and generating an electric potentialdifference between the two ribs 1 and 2, it is possible to induce achange in the refractive index which is caused by changes in the carrierdensity, and to thereby make it possible to vary the opticalcharacteristics of the electrode element.

Note that the imparting of conductivities of opposite polarities (i.e.,P-type or N-type) to the first rib 1 and the second rib 2, and also theprovision of the electrode pad to impart voltage are not essentialstructure in the present embodiment, and it is also possible to use thecores 1 and 2 without imparting any external voltage thereto.

The above-described cores 1 and 2 and the gap portion 3 are located onthe bottom cladding 6 which is formed as a film on the substrate 5. Thetop of the core is covered by the top cladding 7. The top cladding 7 andthe bottom cladding 6 are formed from a material having a lowerrefractive index than that of the core. Both the materials used to formthe top cladding 7 and the bottom cladding 6 are not particularlyrestricted. Specific examples thereof include Si for the material of thesubstrate 5, and SiO2 for the materials of the top cladding 7 and bottomcladding 6. However, the present embodiment is not particularly limitedto these materials. The top cladding 7 and the bottom cladding 6 have asuitable thickness to correspond to the thickness of the core.

According to the planar optical waveguide element of the presentembodiment, because the mode field diameter of the fundamental modeexpands in a core which is formed from a high refractive index material,it is possible to inhibit the effects (i.e., scattering loss) on theoptical characteristics from roughness of the core-side walls which isunavoidably generated in the manufacturing process.

Second Exemplary Embodiment of a Planar Optical Waveguide Element

FIG. 2 typically shows a cross-sectional view of a second embodiment ofthe planar optical waveguide element 4A of the present invention. Thisplanar optical waveguide element is constructed in the same way as thefirst embodiment shown in FIG. 1A in FIG. 1B except for the fact thatthe core of the optical waveguide is not a rib structure (i.e., anL-shaped structure), but is a rectangular waveguide having a rectangularcross-section.

Specifically, the first and second areas 1A and 2A of the core haverectangular cross-sections each having a height of t₃ and a width of w₃.The first and second areas 1A and 2A are formed from a material having ahigher refractive index than that of the gap portion 3A. The heights ofthe first and second areas 1A and 2A and the height of the gap portion3A are the same, and the heights are indicated in FIG. 2 by t₃. Thewidth of the gap portion 3A is w₄, and the gap portion 3A is formed froma material having a lower refractive index than that of the first andsecond areas 1A and 2A.

According to the planar optical waveguide element of the presentembodiment, because the mode field diameter of the fundamental modeexpands in a core which is formed from a high refractive index material,it is possible to inhibit the effects (i.e., scattering loss) on theoptical characteristics from roughness of the core-side walls which isunavoidably generated in the manufacturing process.

[Example of a Grating Structure]

In the planar optical waveguide elements in the above describedembodiments, it is possible to provide a grating structure based oncyclical variations in the core shape and dimension. If a gratingstructure is provided, as is described below, an outer side core may beprovided on top of the ribs 1 and 2 and the gap portion 3, and a Bragggrating pattern may be provided on the side wall or top portion of thisouter side core. An example of the method used to design the Bragggrating pattern involves specifying three factors, namely, wavelengthdispersion, wavelength slope, and reflectance as parameters, and thencalculating a predetermined complex reflectance spectrum. Next, a shapedistribution of the effective refractive index which extends in (along)the waveguide direction of an optical waveguide having a Bragg gratingis obtained from this complex reflectance spectrum and the desiredoptical waveguide length.

Bragg grating patterns may be provided on both the side wall and topportion of the outer side core, as this makes it possible to reduce thepolarization dependence of the optical characteristics by these twoBragg grating patterns. Therefore, hereinafter, exemplary embodimentsand design methods of a planar optical waveguide element having twoBragg grating patterns on the optical waveguide will be described.

An example of a grating structure in the planar optical waveguideelement of the present invention is shown in FIG. 3A through FIG. 3C. Ifthe width or thickness of the waveguide in the light propagationdirection is changed cyclically in an optical waveguide, then theeffective refractive index of the optical waveguide also changescyclically, and a Bragg grating can be constructed. In FIG. 3A throughFIG. 3C, only the core 10 is shown and the claddings are not shown,however, it is to be assumed that cladding surrounds the periphery ofthe core 10. In addition, a substrate (not shown) is located below thecladding, and a bottom surface 14 of the core 10 is parallel with thesubstrate surface. The term “horizontal direction” refers to a directionwhich is parallel to this substrate surface, and the term “verticaldirection” refers to a direction which is perpendicular to the substratesurface. If this grating structure is applied to a planar opticalwaveguide element of an exemplary embodiment, then it may be appliedwith this core 10 being used as an outer side core.

FIG. 3A is a plan view of a portion of the core 10. The symbol Crepresents a single center axis within a horizontal plane of the opticalwaveguide core 10, and light is propagated along this center axis Cwithin the optical waveguide. This optical waveguide has a Bragg gratingpattern (described below in detail), and at least one reflection band isevident in the spectrum of this optical waveguide. A center wavelengthλ₀ of this reflection band is determined by λ₀=2 p_(G)/n_(eff) when thecycle of the Bragg grating is taken as p_(G), and the effectiverefractive index of the optical waveguide is taken as n_(eff). Here, theeffective refractive index n_(eff) is the value when the width of thecore 10 of the optical waveguide is taken as an average width w₀.

The average width w₀ of the core 10 is equivalent to the average valuein one cycle of the horizontal width w_(out) of the core 10, and is aconstant value (same value) along the center axis C over the entireoptical waveguide. Recessed portions 12 a and protruding portions 12 bare formed alternatingly in a side wall 12 of the core 10, and thehorizontal width w_(out) oscillates alternatingly for each cycle p_(G)so as to form a first Bragg grating pattern. This Bragg grating patternis regarded as one in which the width (namely, the horizontal widthw_(out)) in the horizontal direction of an optical wave guide having arectangular cross-section (see FIG. 3B) changes alternatingly.

Intrinsic waveguide modes exist respectively for both when an electricfield of linearly polarized light extends principally in a horizontaldirection (referred to below as TE-type polarization), and when itextends principally in a vertical direction (referred to below asTM-type polarization) in an optical waveguide having a rectangularcross-section. In addition, polarization dependence also exists in whichintrinsic effective refractive indices are present in each waveguidemode.

An effective refractive index n_(eff) ^(TE) of the intrinsic mode inTE-type polarization changes more responsively in response to changes inthe width of the optical waveguide compared to an effective refractiveindex n_(eff) ^(TM) of the intrinsic mode in TM-type polarization. Incontrast, the effective refractive index n_(eff) ^(TM) of the intrinsicmode in TM-type polarization changes more responsively in response tochanges in the height (namely, the thickness) of the optical waveguidecompared to the effective refractive index n_(eff) ^(TE) of theintrinsic mode in TE-type polarization.

Accordingly, as is shown in FIG. 1A and FIG. 1B, if no Bragg gratingpattern is provided in the gap portion 3 of the optical waveguide core1, and the recessed portions and protruding portions 2 a and 2 b areprovided in the side wall 2 so that only the width of the core 1 ischanged cyclically, then there is a considerable increase inpolarization dependence. Accordingly, in order to reduce thepolarization dependence of the Bragg grating, not only is the width ofthe optical waveguide cyclically changed, but also the height of theoptical waveguide is cyclically changed.

Because of this, in this planar optical waveguide element, two Bragggrating patterns are positioned in mutually different areas on across-section that is perpendicular to the light waveguide direction.

In addition, two Bragg grating patterns are formed in areas that bothextend in parallel with the light waveguide direction. Namely, theranges in which the respective Bragg grating patterns are locatedextending in the direction of the center axis C are the same.

As a result, by combining a first Bragg grating pattern with a secondBragg grating pattern, the effect thereof on TE-type polarization andthe effect thereof on TM-type polarization are made equal, andpolarization dependence can be reduced.

If the application of this to a rectangular optical waveguide (i.e., anoptical waveguide having a substantially rectangular cross-section) isconsidered, then the first Bragg grating pattern may be provided oneither one or both side walls of the core, and the second Bragg gratingpattern may be provided on at least one of the top surface and bottomsurface (on the top surface and/or the bottom surface) of the core. Inthe present embodiment, in order to simplify the formation of the coreon a substrate, the first Bragg grating pattern is provided on both sidewalls of the core, and the second Bragg grating pattern is provided onthe top surface of the core. The shape of the core 10 is symmetrical(i.e., symmetrical above and below the center axis C in FIG. 3A) in ahorizontal direction relative to a plane that extends in the verticaldirection and includes the center axis C.

In order to form an optical waveguide having a Bragg grating on asubstrate, the following manufacturing process is followed.

Firstly, a material used to form the bottom cladding is formed (coated)on one surface of the substrate as a film. Next, a material used to formthe core is formed on the bottom cladding as a film, and this film isthen processed into the shape of the Bragg grating. Thereafter, amaterial used to form the top cladding is formed on the bottom claddingand the core as a film, so that when viewed in cross-section, the coreis enclosed by a bottom cladding and a top cladding.

As is described below, the amplitude and cycle of cyclical variations inthe Bragg grating become non-uniform in order to provide wavelengthdispersion compensation in a plurality of wavelength channels.Accordingly, a forming process may be performed on the core to form itinto a shape that is able to deal with this type of non-uniform cyclicalvariations. Forming process of the core in the width is achieved byetching and lithography (drawing) using an optical mask that contains agrating pattern (i.e., a cyclical variation of the horizontal widthw_(out)) that provides wavelength dispersion compensation for aplurality of channels.

In contrast, it is difficult for the depth of etching which is intendedto form the height of the core to be changed in accordance with theBragg grating pattern. Namely, it is necessary to achieve a cyclicvariation in etching depth in order to form a grating pattern (i.e., acyclical variation in the core height) on the top portion of the core byetching. However, if depth variations in etching within a horizontalplane extending along the substrate surface which are non-uniform andnon-controllable are disregarded, then etching depths are substantiallyuniform (same) under the same conditions. Accordingly, it is difficultto forming process the height of a core in accordance with a Bragggrating pattern.

FIG. 3B shows a cross-section of a core in a plane that intersects thecenter axis C. In the core 10 of the present embodiment, instead ofchanging the height of the core, as is shown in FIGS. 3A through 3C, thewidth w_(in) of a groove 13 provided in a top portion of the core iscyclically changed. The core height is t_(out), and the depth of thegrooves is t_(in). As is shown in FIG. 3A, the groove 13 extends in adirection along the center axis C, and coordinates in the horizontaldirection of the center point of the width w_(in) of the groove 13 arepositioned on the center axis C.

As a result of this, it is possible to make changes to the effectiverefractive index that are the equivalent of cyclically changing theheight of the core 10. Recessed portions 13 a and protruding portions 13b are formed alternatingly in side walls of the groove 13, and thegroove width w_(in) oscillates alternatingly each one cycle p_(G) so asto form a second Bragg grating pattern. Because the depth t_(in) isuniform within the groove 13, it is possible to achieve a groove 13having a cyclic variation in the width w_(in) by using etching andlithography using an optical mask.

According to this type of method, by performing forming process on thewidth w_(in) of a groove provided in a top portion of the core in thesame way as the core width w_(out), it is possible to construct anoptical waveguide having a Bragg grating in both a width direction andheight direction. Accordingly, it is possible to reduce polarizationdependence by matching changes in the effective refractive index whichare generated by the first Bragg grating pattern in the width directionwith changes in the effective refractive index which are generated bythe second Bragg grating pattern in the height direction.

In the structure shown in FIGS. 3A through 3C, in the light waveguidedirection, the wide portions (i.e., the protruding portions 12 b) of thecore width w_(out) of the sidewalls 12 correspond to the narrow portions(i.e., the protruding portions 13 b) of the groove width w_(in) of theinner side walls of the grooves 13, and the narrow portions (i.e., therecessed portions 12 a) of the core width w_(out) of the sidewalls 12correspond to the wide portions (i.e., the recessed portions 13 a) ofthe groove width w_(in) of the inner side walls of the groove 13. Inthis manner, the protrusions and recessed portions of the first Bragggrating pattern are synchronized with the protrusions and recessedportions of the second Bragg grating pattern, so that the pitches (localcycle) p_(G) of each one coincide (same). Employing this simplifies thedesigning of the optical waveguide dimensions.

In order to generate changes that are equivalent to changes in theheight of the core, it is also possible to provide projections (ridges)15, as is shown in FIGS. 4A through 4C, instead of the grooves 13 as thestructure which is provided on the top portion of the core. The grooves13 may be used from the standpoint of ease of controlling the effectiverefractive index, however, if restrictions on materials or processingconditions or the like exist, then it is also possible to select theprojections 15. The projections 15 can be constructed by forming anotherlayer of film from the same material which is used to form the core, andthen forming cyclical variations in the width direction using opticallithography and etching.

In the structure shown in FIGS. 4A through 4C, in the optical waveguidedirection, the wide portions (i.e., the protruding portions 12 b) of thecore width w_(out) of the side wall 12 correspond with the wide portions(i.e., the protruding portions 15 b) of the width w_(in) of theprojections 15, and the narrow portions (i.e., the recessed portions 12a) of the core width w_(out) of the sidewalls 12 correspond with thenarrow portions (i.e., the recessed portions 15 a) of the width w_(in)of the projections 15. In this manner, the cycle of the protrusions andrecessed portions of the first Bragg grating pattern are synchronizedwith the cycle of the protrusions and recessed portions of the secondBragg grating pattern, so that the pitches p_(G) of each coincide.Employing this simplifies the designing of the optical waveguidedimensions.

At least one of the grooves 13 and projections 15 (the grooves 13 and/orthe projections 15) are preferably formed in the center in the widthdirection of the core 10 and on the top portion in the verticaldirection thereof. In this case, the coordinates in the horizontaldirection of the center point of the width w_(in) of the grooves 13and/or projections 15 are located on the center axis C of the core 10.Moreover, it is also possible to form the second Bragg grating patternby combining groove-shaped structural elements with projection shapedstructural elements.

The grooves 13 and projections 15 shown in FIGS. 3A through 3C and FIGS.4A through 4C are connected in the light waveguide direction, however,it is also possible to provide a cyclical change in the core heightdirection by forming at least one of recessed portions and protrudingportions in each pitch. The grooves 13 and projections 15 that areformed on the top surface 11 of the core 10 are formed in a portion ofthe center in the width direction of the core 10, but it is alsopossible for the thickness of the core 10 itself to be changed.

Among these structures, from the standpoint of the manufacturing processa cyclical change in the height direction of the core may be providedusing changes in the width direction of the structural elements on thetop portion of the core. In particular, as is shown in FIGS. 3A through3C and FIGS. 4A through 4C, the second Bragg grating pattern may beformed by at least one of the projection shaped structures 15 and thegroove-shaped structures 13 which are formed in the center in the widthdirection of the core 10 and on the top portion in the verticaldirection thereof. The groove-shaped structures 13 can be obtainedsimply by forming a single layer of film of the material used to formthe core.

Third Exemplary Embodiment of a Planar Optical Waveguide Element

An optical wave guide having a cross-sectional structure such as thatshown in FIG. 5 can be given as an example of a Bragg grating opticalwaveguide structure in which polarization dependence has been reduced.On account of the simplified description of the principle of reducingpolarization dependence, the cross-sectional structures of the cores 10are all the same in the planar optical waveguide elements shown in FIGS.3A through 3C and FIGS. 4A through 4C. However, if the effectiverefractive index is changed by changing the dimensions of the opticalwaveguide, then an optical waveguide having a composite core structuresuch as that shown in FIG. 5 may improve the accuracy of the effectiverefractive index.

The core of the planar optical waveguide element 20 having thecross-sectional structure shown in FIG. 5 is a composite core formed bytwo areas, namely, inner side cores 21 and 22 and an outer side core 24.

In this example, the inner side core is formed by two areas, namely, afirst rib 21 and a second rib 22, and a center gap 23 is providedbetween these two ribs. The first rib 21 and second rib 22 are formedfrom a material having a higher refractive index than that of the outerside core 24. It is not necessary for the center gap 23 to be formedfrom a material having a higher refractive index than that of the outerside core 24. The heights of the first and second ribs 21 and 22 and theheight of the center gap 23 are equal, and the heights are indicated byt2 in FIG. 5. If the center gap is inserted between the first rib 21 andsecond rib 22, then it is possible to increase the cross-sectional areaof the region in which light is confined in the inner side core, whilemaintaining the condition in which only a single mode is present in asingle polarization state. Moreover, because it is possible to reducethe accuracy deterioration of the effective refractive index which isdue to machining errors of the Bragg grating which is formed on theouter side core 24 (described below), this example is also effective inreducing the polarization dependence of the effective refractive index.

The first rib 21 and second rib 22 have the same shape, and a protrudingportion is formed by the mutually abutting portions of each one.Specifically, the first rib 21 and second rib 22 are formed by planarportions 21 a and 22 a which have a thickness of t2, and by rectangularparallelepiped portions 21 b and 22 b which have a height t1 and a widthw1 and which are positioned on edges of the planar portions 21 a and 22a. The material used to form the rectangular parallelepiped portions 21b and 22 b is the same as the material used to form the planar portions21 a and 22 a. The width of the center gap 23 is w2, and the center gap23 is formed from a material having a lower refractive index than thatof the first rib 21 and second rib 22.

Examples of t₁, t₂, w₁, and w₂ are: t₁=250 nm, t₂=50 nm, w₁=280 nm, andw₂=160 nm. However, exemplary embodiments are not limited to thesedimensions.

One example is a combination in which the first rib 21 and second rib 22are formed from silicon (Si), and the center gap 23 is formed fromsilica (SiO₂). Instead of forming the center gap 23 from silica (i.e.,silicon oxide), it may also be formed from silicon oxynitride(SiO_(x)N_(y)) or silicon nitride (Si_(x)N_(y)). Materials in which thecomposition ratio x:y is controlled such that, for example, inSiO_(x)N_(y) the refractive index is 1.5, and in Si_(x)N_(y) therefractive index is 2.0 may be used. However, other composition ratiosmay also be used provided that they have a lower refractive index thanthat of the Si of the high refractive index ribs 21 and 22.

P-conductivity or N-conductivity may be imparted to the first rib 21 orthe second rib 22 by doping the medium with suitable impurities. Namely,the first rib 21 may be set as a P-type area, while the second rib 22may be set as an N-type area. Conversely, the first rib 21 may be set asan N-type area, and the second rib 22 may be set as a P-type area.

The impurities (i.e., dopants) that impart conductivity to the highrefractive index core which is formed by a semiconductor can beappropriately selected in accordance with the maternal medium. Forexample, if the maternal medium is a group-IV semiconductor such assilicon, then a group-III element such as boron (B) can be used as adopant to impart P-type polarity, and a group-V element such asphosphorus (P) or arsenic (As) can be used as a dopant to impart N-typepolarity.

In this manner, by making the first rib 21 and second rib 22 of the corehigh refractive index ribs which are formed from a semiconductor such asSi or the like, and by making one of these ribs a P-type and the otherone a N-type and mutually separating these by the center gap 23 which isformed from an insulating material, a P-I-N bond is formed within aplane represented by the thickness t2 of the inner side cores 21 and 22.In addition, by providing an electrode pad that imparts voltage to boththe first rib 21 and the second rib 22, and thereby generating anelectric potential difference between the two ribs 21 and 22, it ispossible to induce a change in the refractive index which is caused bychanges in the carrier density, and to thereby make it possible to varythe optical characteristics of an electrode element. Moreover, byproviding the center gap 23 which is formed from an insulating materialbetween the two ribs 21 and 22 that make up P-type and N-type areas, theeffect is obtained that it is possible to prevent leakage currentbetween the P-type areas and the N-type areas, and it is also possibleto considerably reduce the current consumption. Specifically, whenvoltage of several V was applied between the two ribs in a structure inwhich there was no center gap, a sub-milliamp (sub-mA) current flowedbetween the P-type and N-type areas. In contrast to this, when a centergap was provided, even when 30 to 40 V of voltage was applied, theleakage current between the P-type and N-type areas are only asub-nanoamp (sub-nA) range.

Note that the imparting of conductivities of opposite polarities (i.e.,P-type or N-type) to the first rib 21 and the second rib 22, and alsothe provision of the electrode pad to impart voltage are not essentialstructure in the present embodiment, and it is also possible to use theinner side cores 21 and 22 without imparting any external voltagethereto.

The outer side core 24 is placed on top of the inner side cores 21 and22. The refractive index of the outer side core 24 is lower than theaverage refractive index of the inner side cores 21 and 22. Examples ofthe material used for the outer side core 24 include Si_(x)N_(y), butother materials may also be used. Although omitted from FIG. 5, the samefirst and second Bragg grating patterns as those formed on the core 10shown in FIGS. 3A through 3C are formed on a top surface 24 a and sidewalls 24 b of the outer side core 24.

Specifically, there are provided a first Bragg grating pattern in whichthe width w_(out) of the outer side core 24 is changed cyclically, and asecond Bragg grating pattern in which the width w_(in) of a groove(trench) 24 c which is formed on the top surface 24 a of the outer sidecore 24 is changed cyclically. The thickness of the outer side core 24is t_(out), and the depth of the groove 24 c is t_(in).

Examples of t_(out) and t_(in) are: t_(out)=600 nm, and t_(in)=100 nm,however, the present embodiment is not particularly limited to thesedimensions. w_(in) and w_(out) change cyclically.

Note that, in the example shown in FIG. 5, the Bragg grating pattern onthe top surface 24 a is formed by the groove 24 c. However, as isdescribed above it is also possible to employ the projections 15 (seeFIGS. 4A through 4C).

The above described composite core is located on the bottom cladding 26which is formed as a film on the substrate 25. The top portion and sidewalls of the composite core are covered by the top cladding 27. The topcladding 27 and bottom cladding 26 are formed from a material having alower refractive index than the average refractive index of thecomposite core. The same material or different materials may be used forthe top cladding 27 and the bottom cladding 26. Specific examplesthereof include using Si for the material of the substrate 25, and usingSiO₂ as the material for the top cladding 27 and bottom cladding 26,however, the present embodiment is not particularly limited to this. Thetop cladding 27 and bottom cladding 26 may have a suitable thickness tocorrespond to the thickness of the composite core. For example, if thedimensions of the composite core are as described above, then thethickness of the bottom cladding 26 is approximately 2000 nm, while themaximum thickness of the top cladding 27 (i.e., the thickness of theplanar portions 21 a and 22 a) is approximately 2000 nm.

If the average refractive index (i.e., the overall average refractiveindex obtained from the two ribs and the center gap combined) of theinner side core is higher than the average refractive index of the outerside core 24, then when light is wave-guided to the composite core,because a greater electric field is present within the inner side core,the proportion of the effective refractive index that is changed byw_(out) and w_(in) is reduced compared with when the core is uniform.Accordingly, even if there are errors in the machining dimensions of theBragg grating pattern formed on the outer side core, any effects of thison the effective refractive index are minimal. Accordingly, it ispossible to increase the accuracy of the effective refractive index. Inmicrofabrication on a flat substrate, errors of approximately 10 nm aregenerally considered. According to a composite core such as that shownin FIG. 5, it is possible to hold the effects on errors in the effectiverefractive index which are due to the machining accuracy to less than 80ppm of the average value of the effective refractive index. Note thatthis term “average value of the effective refractive index” indicatesthe effective refractive index of the optical waveguide at the averagewidth w₀, as is shown in FIG. 3A.

Example 1 of a Wavelength Dispersion Compensation Element

Next, a description will be given of a procedure introduced for thefirst time by the present exemplary embodiment for the design of a Bragggrating optical waveguide having reduced polarization dependence. Therespective steps given below provide an itemized outline of the designflow of this procedure.

[1] The dimensions of the cross-sectional structure of an opticalwaveguide having reduced polarization dependence are specified, and thefield distribution of the intrinsic mode of the TE-type polarization andTM-type polarization in the cross-section are calculated. The effectiverefractive index is calculated from the field distribution of eachintrinsic mode, and correspondence relationships between these effectiverefractive indices and the optical waveguide dimensions which are usedto determine the cross-sectional structure are obtained from theeffective refractive indices.

[2] The desired wavelength dispersion characteristics and reflectioncharacteristics are specified, and the necessary data required fordetermine the structure of the optical waveguide is prepared.

[3] The optical waveguide length is provided, and the shape distribution(profile) of the effective refractive index in a direction extendingalong the center axis C of the optical waveguide is calculated from thewavelength dispersion characteristics and reflection characteristics ofthe above described [2] using an inverse scattering problems solutionmethod.

[4] Based on the correspondence relationships between the effectiverefractive indices and the optical waveguide dimensions obtained in theabove described [1], the shape (i.e., the profile of the opticalwaveguide dimensions in a direction extending along the center axis C ofthe optical waveguide) of the Bragg grating optical waveguide is decidedfrom the shape distribution of the effective refractive index obtainedin [3].

The step [1] through [4] will now be described.

Note that because step [1] only needs to be completed before step [4],it is of course possible for the steps to be performed in the sequence[1]→[2]→[3]→[4], or [2]→[3]→[1]→[4], or [2]→[1]→[3]→[4], or for [1],[2], and [3] to each be performed in parallel.

Namely, this design method includes an optical waveguide cross-sectionalstructure design process (a) which comprises step [1], a Bragg gratingpattern design process (b) which comprises steps [2] and [3], and awavelength dispersion compensation element design process whichcomprises step [4], and the sequence in which process (a) and process(b) are performed is not restricted.

Here, in an optical waveguide structure having the composite core shownin FIG. 5, calculations were made when the first and second ribs 21 and22 were formed from Si, the center gap 23 was formed from SiO₂, theouter side core 24 was formed from Si_(x)N_(y), the substrate 25 wasformed from Si, the bottom cladding 26 was formed from SiO₂, and the topcladding 27 was formed from SiO₂, and t₁=250 nm, t₂=50 nm, w₁=280 nm,w₂=160 nm, t_(out)=600 nm, t_(in)=100 nm, the thickness of the bottomcladding 26 was 2000 nm, and the maximum thickness of the top cladding27 was 2000 nm. Note that the design method of exemplary embodiments canalso be applied to optical waveguide structures having a uniform coresuch as those in FIGS. 3A through 3C and FIGS. 4A through 4C.

(Step [1])

In the case of the present embodiment, the term “optical waveguidedimensions for determining the cross-sectional structure” refers tow_(out) for a first Bragg grating pattern which is made up of recessedportions and protrusions formed in the side wall 24 b, and to w_(in) fora second Bragg grating pattern which is formed in the groove 24 c in thetop surface 24 a. Therefore, w_(out) and w_(in) are specified, and thefield distribution of the intrinsic mode is calculated using a film modematching method (i.e., an FMM method), a finite element method, or abeam propagation method, and an effective refractive index thatcorresponds to the intrinsic mode is determined. As a result of this,the correspondence relationship between w_(out) and w_(in) and theeffective refractive index is obtained.

A portion of this result is shown in FIG. 6A and FIG. 6B. FIG. 6A is agraph showing changes in the effective refractive index relative tow_(in), and FIG. 6B is a graph showing changes in w_(out) whichaccompanies the changes in w_(in). Here, w_(in) and w_(out) are changedsimultaneously. Mode 1 shown in FIG. 6A is TE-type polarization (with apolarization degree of 98% or more), and mode 2 is TM-type polarization(with a polarization degree of 97% or more). According to FIG. 6A, thedifference between n_(eff) ^(TE) and n_(eff) ^(TM) is 20 ppm or less,which is smaller than the amount of change in the effective refractiveindex caused by machining errors. Accordingly, polarization dependencecan be ignored. Hereinafter, the effective refractive index of mode 1 istaken as effective refractive index n_(eff) of this optical waveguide.

Note that, here, it is assumed that the effective refractive index ofmode 1 is used in the following design process. However, because thedifference between n_(eff) ^(TE) and n_(eff) ^(TM) is less than an errorwould be, instead, the effective refractive index of mode 2 may be takenas the effective refractive index n_(eff) of the optical waveguide, orthe average of the effective refractive indices of both mode 1 and mode2 may be taken as the effective refractive index n_(eff) of the opticalwaveguide.

In the present embodiment, the average value of n_(eff) is taken as2.3480. The horizontal axis is set to n_(eff), the left vertical axis isset to w_(in), and the right vertical axis is set to w_(out). A graphshowing the relationship of w_(in) and w_(out) to n_(eff) is shown inFIG. 7. Using these settings, if the n_(eff) of a particular position issupplied, then w_(in) and w_(out) can be determined, and thecross-sectional structure of the optical waveguide in that position isdetermined.

(Step [2])

The wavelength dispersion characteristics requested in the wavelengthdispersion compensation element cancel out (counteract) the wavelengthdispersion of the intended optical fiber transmission path, and have theopposite coding from the wavelength dispersion of the optical fibertransmission path, and have an equivalent absolute value. In the presentexample, the wavelength band of optical signals being transmitted is inthe L band region (1566.31 to 1612.65 nm), and the optical transmissionpath is formed by a dispersion shifted fiber (G653) having a length of40 km, so that the wavelength dispersion to be assigned to thewavelength dispersion compensation element is stipulated. Moreover, inthe intended optical transmission path, it is to be assumed that opticalsignals of 50 channels of an L band ITU grid in which the frequencyinterval is 100 GHz (which is approximately 0.84 nm if converted into awavelength interval) are being transmitted. The bit rate of thetransmitted optical signals is 40 Gbit/s, and the bandwidth usage ofeach channel is 80 GHz. Outside this bandwidth usage, the delay time isstipulated as a fixed value.

A dispersion shifted fiber exhibits anomalous dispersion in the L band,and the group delay time increases as the wavelength lengthens. If thelength of the optical transmission path is 40 km, and the centerwavelength of the bandwidth usage is approximately 1590 nm, then thewavelength dispersion value is 116 ps/nm, and the dispersion slope(i.e., the higher order wavelength dispersion) value is 2.8 ps/nm².

The wavelength dispersion compensation element generates normaldispersion in which the group delay time decreases as the wavelengthlengthens. In order to perform wavelength dispersion compensation on adispersion shifted fiber, it is necessary to make the absolute values ofthe wavelength dispersion and the dispersion slope of the wavelengthdispersion compensation element equal to these values in the dispersionshifted fiber.

If, using the above, the wavelength dependence of the group delay timerequested in the wavelength dispersion compensation element weredepicted in a graph, it would be like that shown in FIG. 8. Within onewavelength channel, because it is necessary to generate a fixedwavelength dispersion and dispersion slope, it is necessary for thegroup delay time to be continuous. However, between the wavelengthchannels, the spectrums of the optical signals are mutually isolatedfrom each other and are independent. Because of this, there is noobstacle even if the group delay time changes non-continuously at theboundaries between the respective wavelength channels. Using thecharacteristic of the group delay time that non-continuous changes arerepeated between wavelength channels, it is possible to superimpose theBragg grating patterns of a plurality of wavelength channels in the samearea of a single optical waveguide.

The characteristics required for a design are the spectrum of the phaseof the reflectance and reflectance intensity of the Bragg gratingoptical waveguide, namely, the complex reflectance spectrum thereof. Thereflectance intensity is flat in the 1570 to 1612.2 nm wavelengthregion, and is set to 85%. The characteristics of the wavelengthdispersion of the Bragg grating optical waveguide are reflected in thephase of the reflectance. The relationship of follow Formula 1 isestablished between the group delay time τ_(d) and the phase φ.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 2} \right\rbrack & \; \\{{\tau_{d}(\lambda)} = {{- \frac{\lambda^{2}}{2\pi\; c}}\frac{\mathbb{d}\;\phi}{\mathbb{d}\;\lambda}}} & \left( {{Formula}\mspace{14mu} 1} \right)\end{matrix}$

Here, the variable λ is the wavelength, the constant π is pi(circumference ratio), and c is the speed of light (within a medium). Byintegrating the two sides of Formula 1, the phase φ is determined fromthe group delay time τ_(d). As a result of the above, the complexreflectance spectrum is obtained and this is used as a predeterminedcharacteristic in the following step [3].

In the present embodiments, designing which uses an amplitudemodulation-type of Bragg grating in which the amplitude of the Bragggrating changes and the phase changes subordinately to the amplitude isimplemented using processing known as coarse graining (described below).In order to simplify this coarse graining, all of the frequency regionsfor which predetermined group delay time characteristics are determinedfrom the frequency point of origin, namely, from 0 Hz are included inthe complex reflectance spectrum used as input data in the design.

(Step [3])

In this step, an effective refractive index profile in a direction alongthe center axis C of a Bragg grating optical waveguide is derived fromthe predetermined complex reflectance spectrum obtained in step [2].Hereinafter, this derivation process will be described.

Firstly, the following formula is obtained using Maxwell's equation foran electrical field E (z) and a magnetic field H (z) on an opticalwaveguide. Here, z is a coordinate along the center axis C of the Bragggrating optical waveguide, and the coordinate point of origin (z=0) isplaced at the starting end of the optical waveguide, while z is at amaximum value at the finishing end. Accordingly, the maximum value of zis the overall length of the Bragg grating optical waveguide.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 3} \right\rbrack & \; \\{\frac{\mathbb{d}{E(z)}}{\mathbb{d}z} = {{\mathbb{i}\omega\mu}_{o}{H(z)}}} & \left( {{Formula}\mspace{14mu} 2} \right) \\\left\lbrack {{Expression}\mspace{14mu} 4} \right\rbrack & \; \\{\frac{\mathbb{d}{H(z)}}{\mathbb{d}z} = {{\mathbb{i}\omega ɛ}_{o}{n_{eff}^{2}(z)}{E(z)}}} & \left( {{Formula}\mspace{14mu} 3} \right)\end{matrix}$

i is an imaginary unit, ω is the frequency, μ₀ is the magneticpermeability (in a vacuum), and ∈₀ is the dielectric constant (in avacuum). In order to construct a coupled mode equation from Formula 2and Formula 3, as in Formula 4 and Formula 5, E (z) and H (z) areconverted into a traveling wave A₊ (z) and a backward traveling wave A⁻(z) in the coupled mode equation. Reflected waves correspond to A⁻ (z).

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 5} \right\rbrack & \; \\{{A_{+}(z)} = {{\frac{1}{2}\left\lbrack \frac{n_{eff}(z)}{n_{av}} \right\rbrack}^{1/2}\left\lbrack {{E(z)} + {\sqrt{\frac{\mu_{o}}{ɛ_{o}}}\frac{H(z)}{n_{eff}(z)}}} \right\rbrack}} & \left( {{Formula}\mspace{14mu} 4} \right) \\\left\lbrack {{Expression}\mspace{14mu} 6} \right\rbrack & \; \\{{A_{-}(z)} = {{\frac{1}{2}\left\lbrack \frac{n_{eff}(z)}{n_{av}} \right\rbrack}^{1/2}\left\lbrack {{E(z)} - {\sqrt{\frac{\mu_{o}}{ɛ_{o}}}\frac{H(z)}{n_{eff}(z)}}} \right\rbrack}} & \left( {{Formula}\mspace{14mu} 5} \right)\end{matrix}$

n_(av) is the average refractive index of the Bragg grating opticalwaveguide, and in the present example n_(av)=2.3480. If the travelingwave (z) and backward traveling wave A⁻ (z) are used, then the coupledmode equation is expressed as is shown in the following Formula 6 andFormula 7.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 7} \right\rbrack & \; \\{{\frac{\mathbb{d}{A_{+}(z)}}{\mathbb{d}z} - {{\mathbb{i}}\;{k(z)}{A_{+}(z)}}} = {{- {q(z)}}{A_{-}(z)}}} & \left( {{Formula}\mspace{14mu} 6} \right) \\\left\lbrack {{Expression}\mspace{14mu} 8} \right\rbrack & \; \\{{\frac{\mathbb{d}{A_{-}(z)}}{\mathbb{d}z} + {{\mathbb{i}}\;{k(z)}{A_{-}(z)}}} = {{- {q(z)}}{A_{+}(z)}}} & \left( {{Formula}\mspace{14mu} 7} \right)\end{matrix}$

Here, the wave number k (z) is expressed in the following Formula (8),and the potential q (z) in the coupled mode equation is expressed inFormula (9). c_(light) is the speed of light (within a vacuum).

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 9} \right\rbrack & \; \\{{k(z)} = {\frac{\omega}{c_{light}}{n_{eff}(z)}}} & \left( {{Formula}\mspace{14mu} 8} \right) \\\left\lbrack {{Expression}\mspace{14mu} 10} \right\rbrack & \; \\{{q(z)} = {{- \frac{1}{2}}\frac{\mathbb{d}\;}{\mathbb{d}z}{\ln\left\lbrack {n_{eff}(z)} \right\rbrack}}} & \left( {{Formula}\mspace{14mu} 9} \right)\end{matrix}$

If the potential q (z) is determined, then the effective refractiveindex profile of the Bragg grating optical waveguide is provided by thefollowing Formula 10.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 11} \right\rbrack & \; \\{{n_{eff}(z)} = {n_{av}{\exp\left\lbrack {{- 2}{\int_{0}^{z}{{q(s)}\ {\mathbb{d}s}}}} \right\rbrack}}} & \left( {{Formula}\mspace{14mu} 10} \right)\end{matrix}$

The overall length z of the Bragg grating optical waveguide is specifiedas 10.2 mm. An estimation of the overall length is performed in thefollowing manner. The speed of light in a vacuum is multiplied by themaximum value of the group delay time that should be generated in theBragg grating optical waveguide, and the result is then divided by theaverage value of the effective refractive indices. The inversescattering method of Non-patent document 2 is applied to the designingof a high refractive index optical waveguide grating pattern, and thepotential q (z) is determined from the complex reflectance spectrum R(λ) using the following process.

Firstly, the solutions of Formula 4 and Formula 5 are expressed as inthe following Formula 11 and Formula 12.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 12} \right\rbrack & \; \\{{A_{+}(z)} = {{\mathbb{e}}^{{\mathbb{i}}\;{kz}} + {\int_{\infty}^{z}{{\mathbb{e}}^{{\mathbb{i}}\;{kz}^{\prime}}{B_{-}\left( {z,z^{\prime}} \right)}\ {\mathbb{d}z^{\prime}}}}}} & \left( {{Formula}\mspace{14mu} 11} \right) \\\left\lbrack {{Expression}\mspace{14mu} 13} \right\rbrack & \; \\{{A_{-}(z)} = {{\mathbb{e}}^{{- {\mathbb{i}}}\;{kz}} + {\int_{\infty}^{z}{{\mathbb{e}}^{{- {\mathbb{i}}}\;{kz}^{\prime}}{B_{+}\left( {z,z^{\prime}} \right)}\ {\mathbb{d}z^{\prime}}}}}} & \left( {{Formula}\mspace{14mu} 12} \right)\end{matrix}$

A₊ (z) and A⁻ (z) are propagated in the +z direction and the −zdirection respectively. The integral terms in Formula 11 and Formula 12show the effects of reflection. The coupled equation is converted intothe following Gel'fand-Levitan-Marchenko equation (Formula 13 andFormula 14) from Formula 11 and Formula 12.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 14} \right\rbrack & \; \\{{{B_{+}\left( {z,y} \right)} + {\int_{- \infty}^{z}{{B_{-}\left( {z,z^{\prime}} \right)}{r\left( {z^{\prime} + y} \right)}\ {\mathbb{d}z^{\prime}}}}} = 0} & \left( {{Formula}\mspace{14mu} 13} \right) \\\left\lbrack {{Expression}\mspace{14mu} 15} \right\rbrack & \; \\{{{r\left( {z + y} \right)} + {B_{-}\left( {z,y} \right)} + {\int_{- \infty}^{z}{{B_{+}\left( {z,z^{\prime}} \right)}{r\left( {z^{\prime} + y} \right)}\ {\mathbb{d}z^{\prime}}}}} = 0} & \left( {{Formula}\mspace{14mu} 14} \right)\end{matrix}$

Here, y=−c_(light)t (wherein t is time), and y<z. r (z) is an inverseFourier transform of the complex reflectance spectrum R (k) which usesthe wave number as a variable, and corresponds to the impulse response.By providing r (z) and solving Formula (13) and Formula (14), q (z) canbe determined. q (z) is provided by the following Formula (15)Expression 16q(z)=−2B_(z,z)  (Formula 15)

If the determined q (z) is applied to Formula (10), then the effectiverefractive index profile n_(eff) (z) is obtained. A graph in which theeffective refractive index profile of the present example is plottedover the entire length of a Bragg grating optical waveguide is shown inFIG. 9. z=0 mm corresponds to the start point (i.e., the incident endand the emission end) of the Bragg grating optical waveguide, whilez=10.2 mm corresponds to the finishing end of the Bragg grating opticalwaveguide. In addition, the amplitude of the effective refractive indexchanges over the entire length of the optical waveguide.

The potential q (z) of Formula 10 and Formula 15 is a real number. As aresult of this, the calculation to transform from the complexreflectance spectrum R (k) to r (z) which provides an impulse response(in other words, a ‘time response’) is a real number type, so that theamplitude changes and the phase changes subordinately to the amplitude.

Note that the inverse scattering method which is based on theGel'fand-Levitan-Marchenko equation of the coupled mode equation isdescribed in the following document.

“An Efficient Algorithm for Solving Zakharov-Shabat Inverse ScatteringProblem”, G. Xiao and K. Yashiro, IEEE Transactions on Antennas andPropagation, 2002, Vol. 50 Issue 6 pp. 807-811.

FIG. 10 is an enlargement of the horizontal axis of FIG. 9, and displaysa portion of a refractive index profile. As is shown in FIG. 10, theeffective refractive index oscillates as a function of the coordinate z,and it is shown that a Bragg grating pattern is formed.

In the amplitude modulation-type Bragg grating of the embodiments of thepresent invention, the Bragg grating pattern is formed as an amplitudemodulation type by changing the amplitude of the Bragg grating. As aresult, it has the characteristic that the coding of the gradient of theenvelope curve of the amplitude of the Bragg grating is inverted. Thephase of the oscillation of the Bragg grating changes subordinately tothe changes in amplitude.

In order to show an example of amplitude modulation, a portion of theeffective refractive index distribution shown in FIG. 9 is enlarged andshown in FIG. 11 together with the envelope curve (the dotted line) ofthe Bragg grating amplitude. The envelope curve is only displayed forthe maximum values of the amplitude. Because the coding is inverted forthe envelope curve for the minimum values of the amplitude at identicalpoints as for the envelope curve for the maximum values, it is onlynecessary to consider the envelope curve for the maximum values. Anarrow indicates the coordinate point on the waveguide where the codingof the gradient of the envelope curve becomes inverted. The codinginversions exhibit precipitous stepped changes or non-continuous changesthat are generated at a single isolated coordinate point.

In contrast to this, in a sampled Bragg grating, when a coding inversionis generated, it is generated via two points and the precipitous steppedchanges or non-continuous changes do not appear. Furthermore, awaveguide region where the amplitude changes continuously to zero ispresent between these two points. In the amplitude modulation-typegrating of the present example, the amplitude of the envelope curve doesnot become zero at an isolated coordinate point where the coding of thegradient of the envelope curve is inverted, and there are no regionswhere the amplitude is continuously zero. Accordingly, it is possiblefor the waveguide length to be made shorter than for a sampled Bragggrating.

A plurality of isolated coordinate points where the coding of thegradient of the envelope curve is inverted are present on the waveguide.In each of these coordinate points, a non-continuous change in the phaseis brought about incidentally. If the phase changes non-continuously,then the pitch changes. Consequently, the pitch takes on a value whichis different from half the value obtained by dividing the centerwavelength at that coordinate point (1590.83 nm) by n_(av). The accuracywith which the coordinate point where the coding of the gradient of theenvelope curve is inverted is specified depends on the discretizedinterval of the coordinate z of the waveguide which is shown by thehorizontal axis. If this interval is taken as ΔP, then the accuracy forspecifying the coordinate point is within a range of ±ΔP. In thismanner, in the amplitude modulation-type Bragg grating of the presentinvention, the coding of the gradient of the envelope curve of theamplitude of the Bragg grating is inverted so that, as a result,coordinate points are present where the pitch changes discretely.

In the present description, in this example and in all the otherexamples, the discretized resolution of the coordinate z refers to thediscretized interval ΔP of the coordinate z.

If the pitch of variations in the effective refractive index over theentire length of the optical waveguide is measured in the effectiverefractive index distribution of the present example, then it can beunderstood that the pitch changes discretely as shown in FIG. 12. Here,the pitch is determined by extracting all of the maximum values of thechanges in the effective refractive index that regulate the pattern ofthe Bragg grating, and using the distance between respective adjacentmaximum values as the pitch. The pitch of the vertical axis is setwithin a range of 200 nm through 450 nm. The pitch value where thefrequency of occurrence is the highest is the main pitch or pitch centervalue, and corresponds to half a value determined by dividing the centerwavelength (1590.83 nm) by n_(av). In the present example, the discretechanges in the pitch are set using ΔP as the minimum unit of change, andwith the amount of increase or decrease from the main pitch being aninteger multiple of ΔP. Accordingly, the amount of discrete change inthe pitch changes in accordance with any changes in the discretizedinterval of the coordinates on the waveguide shown on the horizontalaxis.

The discrete changes in the pitch have the feature that they do notappear in a chirped Bragg grating. In a chirped Bragg grating, the pitchchanges continuously in the light waveguide direction. In a chirpedBragg grating, the amplitude of the Bragg grating also changes at thesame time, however, the changes in the amplitude are confined to beingused for achieving secondary characteristics such as apodization.Important characteristics such as the phase characteristics and numberof channels of the filter reflection spectrum are achieved by changingthe frequency of the Bragg grating in the light waveguide direction. Inthe present step, it is not possible to construct a chirped Bragggrating. In order to construct a chirped Bragg grating, it is necessaryto switch the conversion from the complex reflectance spectrum R (v) toa time response (an impulse response) to a complex number type ofconversion. As a result of this, the q (z) obtained from Formula 15becomes a complex number. If q (z) is a complex number, then whenn_(eff) (z) is determined from q (z), because n_(eff) (z) is a realnumber, it is necessary for only the real portion of q (z) to be used.Accordingly, an amplitude modulation type of Bragg grating has adifferent design method from that used for a chirped Bragg grating andthe two are classified into mutually different categories. Because it iscontrasted with an amplitude modulation type, a chirped Bragg grating isclassified as a frequency modulation type.

In the present description, in this example and in all the otherexamples, the calculation used for the conversion from the complexreflectance spectrum to an impulse response is a real number-type, andis targeted at amplitude modulation-type Bragg gratings. The conditions(details thereof are given in the following supplement) that are used toselect an amplitude modulation-type Bragg grating are set such that, thediscretized resolution of the coordinate axis, namely, the samplingcycle is not less than the amount of change in the pitch whichcorresponds to a half value of the width of the reflection band, usingcoarse graining. In other words, the sampling cycle is not less than themaximum value of the amount of change from the center value of the pitchin a chirped Bragg grating.

At this time, the following two conditions may be met: (I) The frequencyrange of the specified spectrum characteristics includes all the regionsfrom the point of origin (i.e., a frequency of 0) to the region wherethe relevant spectrum channel is located; (II) A real number type isselected in the above described conversion from the complex reflectancespectrum to an impulse response.

Here, the reason for this is that, because (I) simplifies the coarsegraining, and because (II) is not targeted at chirped Bragg gratings, itis not necessary to select a complex number type in which the processingis complicated.

Five discrete values are taken for the pitch value, and the frequencywith which these values are taken is concentrated in the three valuesformed by the center value and by the values above and below the centervalue. In FIG. 12, regions which include the three values are shown onthe vertical axis. Among these, the frequency with which the centerpitch (340 nm) is taken is the highest, and this becomes the main pitch.An average value of the minimum value (272 nm) and the maximum value(408 nm) of the pitch within the range of the vertical axis shown inFIG. 12 coincides with the main pitch. If the center wavelength iscalculated with the product of the average value (2.3480) of theeffective refractive index and the main pitch providing the half valueof the center wavelength of the reflection band of the Bragg grating,then this center wavelength is 1597 nm which substantially coincideswith the center of the wavelength band shown in FIG. 8. Accordingly, therepetition of a change either +68 nm or −68 nm from the main pitchbecomes the principal cause for wavelength dispersion being generated ina plurality of wavelength channels around the center wavelength. As aresult of this, the Bragg grating pattern of the present example isformed as a result of the pitch changing discretely at the same time asthe amplitude changes continuously.

Taking a limited number (i.e., a low number) of discrete values as thepitches is effective in maintaining the frequency of work in themanufacturing process on a planar substrate. A grating pattern ismanufactured based on pattern lithography using an optical mask. If thepitch changes continuously, it is difficult to maintain the accuracy ofthe optical lithography over all the pitches, and there is a concernthat the pattern of a chirped Bragg grating will differ from the design.If the changes in pitch are limited to a small discrete value, thenoptimizing the lithography conditions is easy and the accuracy of thelithography is not adversely affected. Accordingly, the design method ofthe present example is suitable for applications in which an opticalwaveguide is manufactured on a planar substrate.

The wavelength dispersion characteristics of a Bragg grating opticalwaveguide having the effective refractive index profile shown in FIG. 9was reproduced by simulation, and it was confirmed that they matched thecharacteristics (see FIG. 8) used as input data. The confirmedsimulation was executed as a direct problem in which the effectiverefractive index profile shown in FIG. 9 was assigned to the coupledmode equations of Formula 6 and Formula 7. When Formula 1 was applied tothe phase component of the complex reflectance spectrum which was theresult thereof, then the wavelength dependence of the group delay timewas obtained as is shown in FIG. 13A. When FIG. 13A was compared withFIG. 8, it was found that predetermined wavelength dispersioncharacteristics were reproduced.

(Step [4])

Based on a correspondence relationship between the dimensions and theeffective refractive index of the optical waveguide prepared in Step[1], the effective refractive index profile determined in Step [3] wasconverted into distribution data (i.e., profile) of the dimensions ofthe optical waveguide. When the effective refractive index was provided,w_(out) and w_(in), which are the dimensional parameters to be decided,were determined. Accordingly, by associating w_(out) and w_(in) with theeffective refractive index at each point of the coordinates z,distribution data was obtained for the optical waveguide dimensionsw_(out) and w_(in).

The Bragg grating pattern shown in FIG. 10 has a sinusoidal shape. In apattern transfer process which is based on dry-etching and lithographyusing an optical mask, if a rectangular wave type of shape is employedin which a repeated combination of spaces whose lines, which have afixed width, and widths change in accordance with the pitch is arranged,there are few fluctuations in the shape after the dry etching.Therefore, after profile data for the optical waveguide dimensionsw_(out) and w_(in) has been obtained from the profile of the effectiverefractive index, it is converted into a rectangular wave-shapedprofile. However, in this conversion to a rectangular wave shape, thefollowing two restrictions must be observed.

(1) The line width is fixed to 180 nm (the space changes in accordancewith the pitch).

(2) The line amplitude of the rectangular wave shape line is adjusted soas to match the core surface area covered by the sinusoidal Bragggrating pattern.

In accordance with the above flow, the profiles of w_(out) and w_(in)shown in FIG. 14 are obtained. The range of the horizontal axis in FIG.14 is in the same region as the horizontal axis in FIG. 10. Because agroove is provided in the top portion of the core, and the width of thegroove is changed in accordance with the Bragg grating pattern, anantiphase type of change is exhibited in which as w_(out) increases,w_(in) decreases. If projections are provided on the top portion of thecore, and the width of the projections is changed in accordance with theBragg grating pattern, then a normal phase type of change is exhibitedin which as w_(out) increases, w_(in) also increases.

A procedure for manufacturing a Bragg grating optical waveguide havingreduced polarization dependence is described above using Steps [1]through [4]. It is estimated that the element length is less than halfthe length when an optical fiber Bragg grating is used. By manufacturingan optical waveguide based on the above description, it is possible toprovide a small-sized wavelength dispersion compensation element havingreduced polarization dependence. Because the optical waveguide is areflective type, light which is input from z=0 is propagated along theBragg grating optical waveguide, and is propagated inversely from theinput direction and is output from z=0. Note that as long as Step [1] isexecuted prior to Step [4], Step [1] may be executed after either one ofStep [2] or Step [3].

If both w_(out) and w_(in) are not changed simultaneously and only oneis changed, then it is not possible to reduce the polarizationdependence, and the difference between n_(eff) ^(TE) and n_(eff) ^(TM)increases to approximately 1000 ppm at maximum, which is approximately50 times the difference in the present example. As is shown in FIG. 13Bthrough FIG. 13D, a linear relationship is maintained between the groupdelay time and the wavelength, and variations in the group delay timewhich accompany variations in the change increase by approximately afactor of 50 compared with the present example. Namely, using thepresent example, in a wavelength dispersion compensation element whichemploys a high refractive index optical waveguide, it is possible toreduce the polarization dependence of the wavelength dispersion toapproximately 1/50^(th).

The Bragg grating optical waveguide described in the present example canalso be used for wavelength dispersion compensation in other wavelengthregions. As an example of a wavelength dispersion compensation elementin another wavelength band, a case in which a C-band region is targetedis provided in another example.

Reference Example of a Planar Optical Waveguide Element

The cross-sectional structure of a planar optical waveguide element ofthe present reference example is shown in FIG. 15. The core of a planaroptical waveguide element 30 which has the cross section shown in FIG.15 is a composite core formed by two areas, namely, inner side cores 31and 32 and an outer side core 34. The present example is the same as thethird example shown in FIG. 5 except for the fact that the inner sidecores 31 and 32 do not have a center gap. The structures of the outerside core 34, of a first Bragg grating pattern which is formed on a sidewall 34 b of the outer side core 34, of a second Bragg grating patternwhich is formed in a groove 34 c in a top surface 34 a, and of asubstrate 35, a bottom cladding 36, and a top cladding 37 are the sameas in the third example shown in FIG. 5.

In this example, the inner side cores 31 and 32 are formed as two areas,namely, a first rib 31 and second rib 32, and a central gap is notprovided between the two ribs. The first and second ribs 31 and 32 areformed from a material having a higher refractive index than that of theouter side core 34. The first rib 31 and second rib 32 are the sameheight, and this height is indicated by t₂ in FIG. 15. The first andsecond ribs 31 and 32 each have an identical shape, and are shaped so asto be the reverse of each other in a horizontal direction. Specifically,the first and second ribs 31 and 32 are formed by planar portions 31 aand 32 a which each have a thickness of t₂, and by rectangularparallelepiped portions 31 b and 32 b which have a height t₁ and a widthw₁, and which are positioned on edges of the planar portions 31 a and 32a. The material used to form the rectangular parallelepiped portions 31b and 32 b is the same as the material used to form the planar portions31 a and 32 a. The first rib 31 and the second rib 32 are joined via acenter joining portion 33.

Because the cross-sectional area of the inner side core is reduced dueto there being no center gap, variations in the effective refractiveindex which are caused by size variations in the first and second ribs31 and 32 are increased. However, because it is possible to omit themanufacturing process which is performed in order to provide the centergap, the manufacturing process can be simplified and both a shorteningof the manufacturing period and a reduction in costs can be achieved. Ifa shortening of the manufacturing period and a reduction in costs aregiven precedence over the performance of the element, then the structureof the present reference example can be used.

In the planar optical waveguide element of the present referenceexample, in the same way as in the above described third example,P-conductivity or N-conductivity may be imparted to the first rib 31 andthe second rib 32 by doping the medium with suitable impurities. It isalso possible to provide electrode pads that impart voltage to both thefirst rib 31 and the second rib 32, and by generating an electricpotential difference between the two ribs 31 and 32, to make it possibleto induce changes in the refractive index which are caused by changes inthe carrier density, and to thereby make it possible to vary the opticalcharacteristics of an electrode element.

Note that the imparting of conductivities having opposite polarities(i.e., P-type or N-type) to the first rib 31 and the second rib 32, andalso the provision of the electrode pad to impart voltage are notessential structure in the present reference example, and it is alsopossible to use the inner side cores 31 and 32 without imparting anyexternal voltage thereto.

Moreover, it is also possible for the first rib 31 and the second rib 32to be formed from an identical material including whether or not dopantsare added thereto. In this case, the center joining portion 33 is notprovided, and the two ribs 31 and 32 are able to form an inner side coreas a single integrated layer.

Reference Example 1 of a Wavelength Dispersion Compensation Element

In the present reference example, a case was calculated as Referenceexample 1 relating to a wavelength dispersion compensation element inwhich, in an optical waveguide structure having the composite core shownin FIG. 15 (having no center gap), the first and second ribs 31 and 32were formed from Si, the outer side core 34 was formed from Si_(x)N_(y),the substrate 35 was formed from Si, the bottom cladding 36 was formedfrom SiO₂, the top cladding 37 was formed from SiO₂, and in which t₁=250nm, t₂=50 nm, w₁=100 nm, w₂=160 nm, t_(out)=600 nm, and t_(in)=100 nm,and in which the thickness of the bottom cladding 36 was 2000 nm, andthe maximum thickness of the top cladding 37 was 2000 nm.

In this Reference example 1 as well, in the same way as in Example 1,changes in w_(out) and w_(in) relative to the effective refractive indexwere calculated in accordance with Step [1]. The results thereof areshown in FIG. 16. In this Reference example 1, the average value of theeffective refractive index is 2.2225.

Furthermore, in the same way as in Example 1, a wavelength dispersioncompensation element for 50 channels of an L band ITU grid in which thefrequency interval was 100 GHz was designed in accordance with Steps [2]through [4] for a dispersion shifted fiber having a length of 40 km. Thewavelength dependence of the group delay time to be assigned to thewavelength dispersion compensation element is the same as that shown inFIG. 8 for Example 1. The reflectance was also 85% in a wavelengthregion of 1570-1612.2 nm. Accordingly, as for the predeterminedcharacteristics, the complex reflectance spectrum was the same as inExample 1. The bit rate of the transmitted optical signals was also thesame as in Example 1 at 40 Gbit/s, and the usage band of each wavelengthchannel was regulated to 80 GHz.

The overall length of the Bragg grating optical waveguide was 10.737 mm,and the effective refractive index profile shown in FIG. 17 wasobtained. This profile was the same as the profile shown in FIG. 9 otherthan in the following points. In Reference example 1, the profile isenlarged in the center axis direction and the overall length of theoptical waveguide is extended by the amount that the average value ofthe effective refractive index is smaller than it is in Example 1.

From the relationship shown in FIG. 16, in the same way as in Step [4]of Example 1, profiles of w_(out) and w_(in) were obtained. A portion ofthis is shown in enlargement in FIG. 18. The Bragg grating opticalwaveguide of the present Reference example 1 can also be designed so asto deal with wavelength bands outside the L band. In this case, thecomplex reflectance spectrum to be determined in the relevant wavelengthband is determined in accordance with Step [2] described in Example 1,and the shape is designed in accordance with Steps [3] and [4].

Example 2 of a Wavelength Dispersion Compensation Element

Next, in the same way as in Example 1, an example of a wavelengthdispersion compensation element for 40 channels ITU grid in which thefrequency interval was 100 GHz in a C band (1528.77 to 1577.03 nm) whichwas designed in accordance with Steps [2] through [4] of Example 1 usinga Bragg grating optical waveguide having the cross-sectional structuredescribed in FIG. 5, is described as Example 2.

The material forming the optical waveguide is the same as in Example 1.The intended optical fiber is a standard dispersion single mode fiber(G652) having a length of 30 km. In a wavelength of 1550 nm, thewavelength dispersion value was 510 ps/nm, and the dispersion slopevalue was 1.74 ps/nm². The bit rate of the transmitted optical signalswas 10 Gbit/s, and the usage band of each wavelength channel was 20 GHz.Outside the usage band, the group delay time was regulated to beuniform. A graph of the wavelength dependence of the group delay timerequired in the wavelength dispersion compensation element is shown inFIG. 19. Here, the range of the horizontal axis is 1533.85 through1565.58 nm. The reflectance is flat within the wavelength region shownby the horizontal axis in FIG. 19 and is 85%.

The length of the Bragg grating optical waveguide was 9.9 mm, and theeffective refractive index profile shown in FIG. 20 was obtained. Thepeak distributed in the vicinity of z=2 mm and the peak distributed inthe vicinity of z=6.5 through 7 mm were present in order to flatten thereflectance and group delay time in regions separate from the usageband. Accordingly, the Bragg grating length which contributes tochanging the group delay time within the 20 GHz usage band at maximumcorresponds to the distance differential between these two peaks, and isthought to be 5 mm or less. However, if the length required by anoptical fiber Bragg grating having the equivalent functions is estimatedbased on the results shown in Non-patent document 1, then it is thoughtto be approximately 10 mm. Accordingly, according to the presentexample, the optical waveguide length required for wavelength dispersioncompensation is shortened to less than half that required by an opticalfiber Bragg grating.

FIG. 21 shows changes in pitch over the entire length in a pitch rangeof 200 to 450 nm. In the same way as in FIG. 12, the frequency withwhich the pitch in the center is taken is the highest, and this formsthe main pitch. Moreover, the average value of the minimum value (i.e.,the next smaller discrete value from the center value) and the maximumvalue (i.e., the next larger discrete value from the center value) ofthe pitch within the vertical axis range shown in FIG. 21 coincides withthe main pitch.

In the same way as in Example 1, by assigning the shape distribution ofthe effective refractive index supplied in FIG. 20 to the coupled modeequations of Formula 6 and Formula 7 and then solving these equations,the wavelength dispersion characteristics shown in FIG. 22 are obtained.If FIG. 22 is compared with FIG. 19, it can be seen that predeterminedwavelength dispersion characteristics are reproduced.

In the same way as in Example 1, by deciding the dimensions of a Bragggrating optical waveguide from the relationships between w_(in) andw_(out) relative to the effective refractive index n_(eff) shown in FIG.7, it is possible to manufacture a small-size wavelength dispersioncompensation element for the C band having reduced polarizationdependence.

Example 3 of a Wavelength Dispersion Compensation Element

Next, in the same way as in Example 1, an example of a wavelengthdispersion compensation element for an L band single channel designed inaccordance with Steps [2] through [4] of Example 1 using a Bragg gratingoptical waveguide having the cross-sectional structure described in FIG.5 is described as Example 3.

The material forming the optical waveguide was the same as in Example 1.The intended optical fiber was a dispersion shifted fiber having alength of 30 km. The reflectance was 85% and the characteristics shownin FIG. 23 were specified for the wavelength dependence of the groupdelay time, so that a predetermined complex reflectance spectrum wasobtained.

The length of the Bragg grating optical waveguide was 8.13 mm, and theeffective refractive index profile (shape distribution) shown in FIG. 24was obtained. The peak of the envelope curve of the changes in theeffective refractive index in the effective refractive index profileshown in FIG. 24 was in the vicinity of z=4.2 mm.

FIG. 25 shows changes in pitch over the entire length in a pitch rangeof 200 to 450 nm. In the case of the present example, the pitch takesonly three values (discrete values outside the range of the verticalaxis do not appear). In the same way as in FIG. 12, the frequency withwhich the pitch in the center (340 nm) is taken is the highest, and thisforms the main pitch. Moreover, the maximum value (i.e., the next largerdiscrete value from the center value) is 68 nm bigger than the centervalue and the minimum value (i.e., the next smaller discrete value fromthe center value) is 68 nm smaller than the center value. The averagevalue of the maximum value and the minimum value coincides with thecenter value which forms the main pitch.

As is shown in FIG. 25, on the front end side and the rear end side ofthe peak position of the effective refractive index, the trend of thediscrete changes in pitch is inverted. On the front end side of the peakposition, the pitch only takes two values, namely, the center value andthe maximum value. In other words, a binary change is exhibited on thelong wavelength side of the center value. In contrast, on the rear endside of the peak position, the pitch only takes two values, namely, thecenter value and the minimum value, and a binary change is exhibited onthe short wavelength side of the center value. Wavelength dispersioncompensation is possible by a pitch change Bragg grating which issimpler than chirped type of Bragg grating in which the pitch changescontinuously. The Bragg grating of Example 1 may be thought to beconstructed by combining a plurality of patterns to the pattern of thepresent example which is used as a foundation.

In the same way as in Example 1, by assigning the profile of theeffective refractive index supplied in FIG. 24 to the coupled modeequations of Formula 6 and Formula 7 and then solving these equations,the wavelength dispersion characteristics shown in FIG. 26 are obtained.If FIG. 26 is compared with FIG. 23, it can be seen that predeterminedwavelength dispersion characteristics are reproduced.

As a result of the above, it is possible to manufacture a wavelengthdispersion compensation element which has reduced polarizationdependence in a single wavelength channel within the L band. Themanufacture of elements used in different wavelength bands can also beachieved by considering the characteristics of the wavelengthdispersions that correspond to each wavelength band, and designing Bragggrating optical waveguides using the ideas of the present example.

[Method of Connecting a Wavelength Dispersion Compensation Element andan Optical Waveguide]

In the wavelength dispersion compensation elements of Examples 1 through3, optical signals emitted from a Bragg grating optical waveguide arepropagated in the opposite direction along the path of incident opticalsignals. Namely, because emitted signal light is propagated along thesame path as incident signal light, a method of separating the emittedsignal light from the incident signal light is required. In the presentexample, as is shown in FIG. 27, a description is given of the structureof a wavelength dispersion compensation element by connecting an opticalcirculator 102 to a wavelength dispersion compensation element 101, inwhich the element has a port where incident signal light is irradiatedonto the wavelength dispersion compensation element, and a port whereemitted signal light is extracted from the wavelength dispersioncompensation element.

If the wavelength dispersion compensation element 101 of the presentexample corresponds to the wavelength dispersion compensation element ofexemplary embodiments described herein, then the wavelength dispersioncompensation element 101 of any of the Examples 1 through 3 may be used,or another element may be used. The optical circulator 102 is connectedto the front end portion side of the wavelength dispersion compensationelement 101. An incident optical fiber 103 that propagates incidentsignal light, a coupling optical fiber 104 that connects together thewavelength dispersion compensation element 101 and the opticalcirculator 102, and an emission optical fiber 105 that propagatesemitted signal light are connected to the optical circulator 102.

Incident signal light is transferred by the optical circulator 102 fromthe incident optical fiber 103 to the coupling optical fiber 104, and isirradiated onto the wavelength dispersion compensation element 101.Emitted signal light that has been reflected inside the wavelengthdispersion compensation element 101 is transferred from the couplingoptical fiber 104 to the emission optical fiber 105 via the opticalcirculator 102. In order to reduce loss which is caused by theconnection between the coupling optical fiber 104 and the wavelengthdispersion compensation element 101, it is preferable for lens machiningto be performed on the distal end of the coupling optical fiber 104(i.e., the distal end thereof on the wavelength dispersion compensationelement 101 side), or for a micro lens to be placed between the couplingoptical fiber 104 and the wavelength dispersion compensation element101, or for the coupling optical fiber 104 to be connected by adhesionto the front end portion of the Bragg grating optical waveguide of thewavelength dispersion compensation element 101. The loss created by theconnection is, for example, approximately 1 dB. Because the loss withinthe optical circulator 102 is approximately 1 dB, the total optical losscreated by the connections of the optical circulator 102 isapproximately 2 dB.

In order to install the structure 100 shown in FIG. 27 on an opticalfiber transmission path that is intended for wavelength dispersioncompensation, it is sufficient for the incident optical fiber 103 to beconnected to the transmitter side of the optical fiber transmissionpath, and for the emission optical fiber 105 to be connected to thereceiver side of the optical fiber transmission path. By doing this, itis possible to construct a small-sized wavelength dispersioncompensation element that can be installed on an optical fibertransmission path, and that has a low level of optical insertion loss.

Example 1 of an Optical Filter

An optical filter having reflection bands in ten mutually differentwavelength channels was constructed using the planar (substrate-type)optical waveguide in the above described Example 3 of a planar opticalwaveguide element. The method used to design the optical filter was madeup of the following steps [1] to [4].

[1] The dimensions (w_(in)/w_(out)) of the cross-sectional structure ofthe optical waveguide core are specified, and the field distribution ofthe intrinsic mode of the TE-type polarization and TM-type polarizationin the cross-section are calculated. These dimensions are then adjustedsuch that the effective refractive indices in the two polarizations areequal. w_(in)/w_(out) are then decided such that polarization dependenceis cancelled out in different effective refractive indices. Thecorrespondence relationship between the effective refractive indices andw_(in)/w_(out) are then obtained so that it is possible to decide thedimensions of the cross-sectional structure of the optical waveguidecore from the effective refractive indices. This step is the designprocess for the cross-sectional structure of the optical waveguide core.

[2] The reflection characteristics desired for the optical filter arespecified, and the necessary data required to determine the structure ofthe optical waveguide is obtained. What are specified as the reflectioncharacteristics are the reflectance and phase in each wavelength. All ofthe frequency regions that include the desired reflectioncharacteristics from the point of origin (i.e., from a frequency of 0Hz) are included in the frequency range.

[3] The optical waveguide length is provided, and the shape distributionof the effective refractive index extending in the waveguide directionof the optical waveguide is derived from the complex field reflectancespectrum obtained in Step [2] using an inverse scattering problemsolution. This step includes a calculation process to convert thecomplex field reflectance spectrum into a time response, however, thisis a real number type of conversion.

Steps [2] and [3] form the Bragg grating pattern design process.

[4] Based on the correspondence relationships between the effectiverefractive indices and the cross-sectional dimensions of the opticalwaveguide core obtained in Step [1], the shape extending in the opticalwaveguide direction of the Bragg grating optical waveguide is decidedfrom the shape distribution of the effective refractive index obtainedin Step [3]. This step forms the optical filter design process.

Note that in the same way as in the above described wavelengthdispersion compensation element design process, the order of these stepscan also be switched.

Hereinafter, each step for designing an optical filter will be describedin detail.

Step [1]

The cross-sectional structure of the waveguide is the same as that shownin FIG. 5.

If the effective refractive index of the TE polarization is regarded asthe effective refractive index of the waveguide, then the graph shown inFIG. 7 is obtained when relationships between the effective refractiveindex and win and wout are calculated and plotted.

Step [2]

The optical characteristics of an optical filter having reflection bandsin ten mutually different wavelength channels were specified. In opticalcommunication, it is common for distinctions to be made between spectrumregions using frequency instead of wavelength. In the present example,hereinafter, the spectrum characteristics of an optical filter as afunction of frequency will be discussed. A complex field reflectancespectrum R (v) is calculated from the reflectance and phase in eachfrequency. In an orthogonal coordinate system, R (v) is formed by a realnumber component and an imaginary number component, however, convertingthe coordinates into a polar coordinate system and splitting the complexfield reflectance into a phase and absolute value of the fieldreflectance simplifies dealing with the optical filter characteristics.Therefore, as in the following Formula A, the complex field reflectanceis expressed using a polar coordinate display.[Expression 17]R(v)=|R(v)|exp[−φ(v)]  (Formula A)

Here, R is the electric field, v is the frequency, |R (v)| is theabsolute value of the field reflectance, and φ (v) is the phase. Theabsolute value of the reflectance is normalized as 1 (namely 100%). Theabsolute value of the field reflectance is set to 0.95 (i.e. 95%) suchthat the power reflectance |R (v)|² becomes 0.9 (90%), within thereflection band of each channel.

In the optical filter of the present example, the wavelength dispersionin the reflection band of each channel is set to zero. If the wavelengthdispersion is zero, the phase forms a linear function relative to thefrequency. As a result of the above, the optical characteristicsspecified for the optical filter of the present example are shown inFIG. 28. In FIG. 28, the left vertical axis shows the absolute value ofthe field reflectance |R (v)|, the right vertical axis shows the phase φ(v), and these are plotted respectively by a solid line and a brokenline. The horizontal axis shows the frequency v in units of THz, andspecifies optical characteristics by dividing the frequency from 192.6THz to 193.6 THz into ten equal channels at intervals of 0.1 THz. Thecenter frequency is 193.1 THz. If this is converted into a centerwavelength, it becomes 1552.52 nm. The spectrum width of the reflectionband in each channel is 0.01 THz, and it can be seen that the phasechanges linearly within this range.

If the spectrum shape of the rectangular reflection band of eachchannel, such as those shown in FIG. 28, is converted into a timewaveform using an inverse Fourier transform, a sinc function type ofimpulse waveform is obtained. If the width of the spectrum of thereflection band is taken as Δv, then the main peak of the sinc functiontype impulse waveform is contained within a time region of approximatelyΔt=3/(Δv). Accordingly, in an optical waveguide that generates areflection band in each channel shown in FIG. 28, the propagation timethat is required between when light is incident and when it is reflectedmust be approximately Δt or even greater than this. The phases, whichchange linearly within the frequency region of each reflection bandshown in FIG. 28, reflect phase delays which are caused by thispropagation time.

FIG. 28 only displays the frequency bands in the vicinity of channelswhere a reflection band is present. All of the frequency bands in whicha reflection channel is present from the point of origin (i.e., from 0THz) are included as desired optical characteristics in the opticalcharacteristics being target of an inverse scattering method. However,because no reflection channels are present in frequency regions outsidethose shown in FIG. 28, the value of the field reflectance is zero.

Step [3]

The effective refractive index distribution in the waveguide directionof the optical waveguide forming an optical filter is derived based onthe inverse scattering problem solution. This procedure is described inStep [3] in the design direction of the above described wavelengthdispersion compensation element.

When specifying the entire length of the optical waveguide, the opticalpath length in accordance with Δt in Step [2] is taken as the minimumvalue, and the specification is made based on the loss and allowabledimensions of the optical waveguide. After the optical waveguide lengthhas been specified, the potential q (z) is determined using an inversescattering problem solution. q (z) is assigned to the above describedFormula 10, and the effective refractive index distribution n_(eff) (z)is obtained. Here, the conversion which is used when an impulse responseis derived from the complex reflectance spectrum R (v) is a real numbertype.

As a result of this, the q (z) which is obtained from the abovedescribed Formula 15 is also a real number, and an effective refractiveindex distribution for an amplitude modulation-type Bragg grating isobtained in which the amplitude of the Bragg grating changes and thephase changes incidentally to the amplitude. A definition of amplitudemodulation in the present invention is given below.

n_(eff) (z) is plotted in FIG. 29 and FIG. 30. The horizontal axis zshows coordinates in the optical waveguide direction. z=0 mm is thestarting end of the Bragg grating optical waveguide, and z=33.0605 mm isthe finishing end thereof. n_(av) which corresponds to the average valueof the refractive index distribution of the grating optical waveguide is2.348 in the present example.

FIG. 30 shows an enlargement of the effective refractive indexdistribution shown in FIG. 29 for a portion of the optical waveguide. Itcan be seen that n_(eff) oscillates at a cycle of half the valueobtained by dividing the center wavelength (1552.52 nm), whichcorresponds to the center frequency (193.1 THz), by n_(av), so as toexhibit a pattern that regulates the Bragg grating.

One of the features of the amplitude modulation-type Bragg grating ofthe present invention is that the coding of the gradient of the envelopecurve of the amplitude of the Bragg grating is inverted. Namely, in thepresent invention, the change when the coding of the gradient of theenvelope curve of the amplitude of the Bragg grating is inverted isknown as amplitude modulation.

The coding inversions exhibit precipitous stepped changes ornon-continuous changes that are generated at a single isolatedcoordinate point, and the characteristic of a sampled Bragg grating thata waveguide region where the amplitude changes continuously to zero isinterposed between two points at which the coding is inverted is notshown. In the amplitude modulation-type grating of the presentinvention, because the amplitude only becomes zero at an isolatedcoordinate point where the coding of the gradient of the envelope curveis inverted, essentially, there are no regions where the amplitude iszero. Accordingly, it is possible for the waveguide length to be madeshorter than in a sampled Bragg grating.

A plurality of isolated coordinate points where the coding of thegradient of the envelope curve is inverted are present on the waveguide.In each of these coordinate points, a non-continuous change in the phaseis generated incidentally. The pitch changes if the phase changesnon-continuously. Consequently, the pitch takes on a value which isdifferent from half the value obtained by dividing the center wavelengthat that coordinate point (1552.52 nm) by n_(av). The accuracy with whichthe coordinate point where the coding of the gradient of the envelopecurve is inverted is specified depends on the discretized interval ofthe coordinate z of the waveguide which is shown by the horizontal axis.If this interval is taken as ΔP, then the accuracy for specifying thecoordinate point is within a range of ±ΔP.

In this manner, in the amplitude modulation-type Bragg grating ofexemplary embodiments, the coding of the gradient of the envelope curveof the amplitude of the Bragg grating is inverted so that, as a result,coordinate points are present where the pitch changes discretely. Thepitch is determined by extracting all of the maximum values of thechanges in the effective refractive index that regulate the pattern ofthe Bragg grating, and using the distance between respective adjacentmaximum values as the pitch. The pitch value where the frequency ofoccurrence is the highest is the main pitch or pitch center value, andcorresponds to half a value determined by dividing the center wavelength(1552.52 nm) by n_(av). In the present example, the main pitch isapproximately 401.2 nm. The discrete changes in the pitch take ΔP as theminimum unit of change, and take the amount of increase or decrease fromthe main pitch as an integer multiple of ΔP. Accordingly, the amount ofdiscrete change in the pitch changes in accordance with any changes inthe discretized interval of the coordinates on the waveguide shown onthe horizontal axis.

The discrete changes in the pitch are the feature that they do notappear in a chirped Bragg grating. In a chirped Bragg grating, the pitchchanges continuously in the light waveguide direction. In a chirpedBragg grating, the amplitude of the Bragg grating also changes at thesame time. However, the changes in the amplitude are confined to beingused for achieving secondary characteristics such as apodization.Important characteristics such as the phase characteristics and numberof channels of the filter reflection spectrum are achieved by changingthe frequency of the Bragg grating in the light waveguide direction. Inthe present step, it is not possible to construct a chirped Bragggrating. In order to construct a chirped Bragg grating, it is necessaryto switch the conversion from the complex reflectance spectrum R (v) toa time response (an impulse response) to a complex number type ofconversion. As a result of this, the q (z) obtained from Formula 15becomes a complex number. If q (z) is a complex number, then whenn_(eff) (z) is determined from q (z), because n_(eff) (z) is a realnumber, it is necessary for only the real portion of q (z) to be used.Accordingly, an amplitude modulation type of Bragg grating has adifferent design method from that used for a chirped Bragg grating andthe two are classified into mutually different categories. Because it iscontrasted with an amplitude modulation type, a chirped Bragg grating isclassified as what is known as a frequency modulation type.

Step [4]

Based on a correspondence relationship between the effective refractiveindex n_(eff) and the dimensions w_(in) and w_(out) of the opticalwaveguide prepared in Step [1], the effective refractive indexdistribution n_(eff) (z) obtained in Step [3] was converted intodistribution data (i.e., profile) of w_(in) and w_(out). When theeffective refractive index was determined by using the correspondencerelationship shown in FIG. 6A and FIG. 6B, w_(out) and w_(in), which arethe dimensional parameters to be decided, were determined. As is shownin FIG. 30, the Bragg grating pattern in the effective refractive indexdistribution has a sinusoidal shape.

In a pattern transfer process which is based on dry-etching andlithography using an optical mask, if a rectangular wave type of shapeis employed in which a repeated combination of spaces whose lines, whichhave a fixed width, and widths change in accordance with the pitch isarranged, there are few fluctuations in the shape after the dry etching.Therefore, after profile data for the optical waveguide dimensionsw_(out) and w_(in) has been obtained from the profile of the effectiverefractive index profile, it is converted into a rectangular wave-shapedprofile. However, in this conversion to a rectangular wave shape, thefollowing two restrictions must be observed.

(1) In the present example, the line width is fixed at 140 nm. Incontrast, the spaces change in accordance with the pitch of the grating.A larger value than the threshold value of the machining accuracy is setfor the line width.

(2) The line amplitude of the rectangular wave shape is adjusted so asto match the core area covered by the sinusoidal Bragg grating pattern.

In accordance with the above flow, the profiles of w_(out) and w_(in)shown in FIG. 31 are obtained. The range of the horizontal axis in FIG.31 is in the same region as the horizontal axis in FIG. 30.

Applications for the optical filter of the present example include, forexample, using it to extract, as non-polarization dependent reflectionlight, only the signal light of wavelength-multiplexed channels afterthis light has passed through the optical amplifier, and to removespontaneous emission optical noise which is present in wavelengthregions adjacent to the signal light. Note that the number of channels,the channel intervals, and the spectrum width of the reflection band arenot limited to the numerical values of the present example, and theoptical filter can be designed with the optimum numerical valuesspecified in accordance with the application.

Example 2 of an Optical Filter

The present example is an example of the design of a beam splitterhaving a power reflectance of approximately 40%. A beam splitter can beused in applications to split the signal light of each channel into twopaths.

The design method of this beam splitter is performed in the same way asthat performed for the optical filter of Example 1, other than the powerreflectance parameters being altered.

The design steps of the present example as well comprise four steps inthe same way as in Example 1. The same correspondence relationshipbetween the effective refractive index and w_(in) and w_(out) in Step[1] as that of Example 1 is used here. In Step [2], the absolute valueof the field reflectance is set to 0.64 (i.e. 64%) such that the powerreflectance within the reflection band of each channel, becomes 0.4(40%). The wavelength dispersion in the reflection band of each channelis set to zero. The optical characteristics specified for the opticalfilter of the present example are shown in FIG. 32. In the same way asin Example 1, the optical characteristics are specified by dividing thefrequency from 192.6 THz to 193.6 THz into ten equal channels atintervals of 0.1 THz.

The center frequency is 193.1 THz. The spectrum width of the reflectionband in each channel is 0.01 THz, and it can be seen that the phasechanges linearly within this range.

The effective refractive index profile of the waveguide derived in Step[3] is shown in FIG. 33 and FIG. 34. The rectangular wave-shaped w_(in)and w_(out) profiles obtained in Step [4] are shown in FIG. 35.

Example 3 of an Optical Filter

The present example is an example of the design of an optical filterhaving a single reflection band. The design steps are the same as inExamples 1 and 2. The power reflectance of the reflection band is set toapproximately 90%. The correspondence relationship between the effectiverefractive index and w_(in) and w_(out) is identical to Examples 1 and2. The specified optical characteristics are shown in FIG. 36. Thespectrum width of the reflection band is 0.01 THz.

The effective refractive index distribution derived based on an inversescattering problem solution using these optical characteristics is shownin FIG. 37 and FIG. 38. The results obtained when the effectiverefractive index was converted to a rectangular wave-shaped profile areshown in FIG. 39. The optical filter of the present example can be usedto extract signal light of a single specific channel as reflectionlight.

Note that the spectrum width of the reflection band is not limited to0.01 THz and it is also possible to design an optical filter with anoptional width specified arbitrarily.

Example 4 of an Optical Filter

The present example is an example of the design of an interleaver for awavelength channel having intervals of 0.1 THz. In the present example,an optical filter is designed with the channel interval set to 0.2 THz,and with the width of the reflection band of each channel set to 0.1THz. The specified optical characteristics are shown in FIG. 40. Theeffective refractive index distribution derived based on an inversescattering problem solution using these optical characteristics is shownin FIG. 41 and FIG. 42. The results obtained when the effectiverefractive index was converted to a rectangular wave-shaped profile areshown in FIG. 43.

The optical filter (i.e., the interleaver) of the present example isable to split the signal light of each channel having an interval of 0.1THz into two paths made up of odd-numbered and even-numbered channels.

[Optical Resonator]

As is shown in FIG. 44, an optical resonator 150 has a structure inwhich optical waveguides which are formed by reflection mirrors 151 and152 (i.e., a first optical waveguide 151 and a second optical waveguide152) are placed at the two ends thereof, and a third optical waveguide153 which includes an optical resonator medium is sandwiched between thereflection mirrors 151 and 152. In the present invention, the firstoptical waveguide 151, the third optical waveguide 153, and the secondoptical waveguide 152 are connected together in series so that a singleplanar optical waveguide is formed, and optical waveguides that have aBragg grating pattern and that have a reflection function are used forthe reflection mirrors 151 and 152 at the two ends thereof. Thedesigning of an optical waveguide having a reflection function can thenbe achieved in accordance with the above described optical filter designmethod by setting the desired reflection characteristics. The thirdoptical waveguide 153 which is formed by an optical resonator medium mayalso have a predetermined optical path length in order for light toresonate between the reflection mirrors 151 and 152.

Because it is desirable to extract light to the outside of theresonator, the reflectance of at least one mirror is lower than 1 (i.e.,100%). For example, as is shown in FIG. 44, in order to emit a portionof the light transmitted from the reflection mirror of the secondoptical waveguide 152, a fourth optical waveguide 154 for emissions isprovided. The fourth optical waveguide 154 is connected in series to thefirst through third optical waveguides so that a single planar opticalwaveguide is formed.

Example 1 of an Optical Resonator

An optical resonator is designed so as to have a function of selectingany one of a plurality of wavelength channels. An example of a pluralityof wavelength channels is an ITU grid having frequency intervals of 100GHz. A description of the optical characteristics of the componentelements of an optical resonator having the required function will nowbe described based on FIG. 45 and FIG. 46. In the graph in the bottomportion of FIG. 45, the power reflection spectrum (the solid line) ofthe first reflection mirror and the power reflection spectrum (thebroken line) of the second reflection mirror are shown.

A spectrum obtained as the product of the power reflection spectrums ofthe first and second reflection mirrors is shown in the graph in the topportion of FIG. 45. The power reflectance of the reflection bands of thefirst and second reflection mirrors is set at 0.9 (i.e., 90%). Thewavelength of the light resonating in the optical resonator is limitedto the region where the reflection regions of the two spectrums overlap.This is generally called a vernier function, and is used in applicationsin which a specific wavelength component is extracted by combining twooptical filters having mutually different comb-like power reflectionspectrums, and, furthermore, is used to make it possible to vary thewavelength components being extracted by varying the characteristics ofone optical fiber.

The resonance characteristics of an optical resonator that includes thefirst and second optical waveguides having the characteristics shown inFIG. 45 are shown in the graph (total) in the top portion in FIG. 46.The vertical axis is shown in a normal logarithmic scale. If it assumedthat the power reflectances of the two end mirrors are notwavelength-dependent and are fixed at 0.9, then the resonancecharacteristics are shown in the graph (FP) in the bottom portion ofFIG. 46. In these resonance characteristics, the resonance peak isnormalized as 1. The optical length of the optical resonator is set to1000 μm. If the effective refractive index of the optical waveguide is1.94945, then the waveguide length obtained by conversion from theoptical length is approximately 513 μm. The resonance characteristicsshown in the graph in the top portion of FIG. 46 are based on a spectrumobtained by superimposing the characteristics of the graph shown in thebottom portion of FIG. 46 onto the spectrum in the graph shown in thetop portion of the FIG. 45. The resonance characteristics in the graphshown in the top portion of FIG. 46 have a peak at 193.1 THz (1552.52nm).

By fixing the effective refractive index of the first optical waveguide,and changing the effective refractive index of the second opticalwaveguide, and changing the pitch of the Bragg grating pattern in thesecond reflection mirror, it is possible to select wavelength componentsof different single channels for the reflection spectrum of the firstreflection mirror using a vernier function. Namely, by changing theeffective refractive index of the second optical waveguide, the selectedwavelength can be varied. Of course, it is also possible to change theeffective refractive index of the first reflection mirror, or to changethe effective refractive indices of both reflection mirrors. In thegraph shown in the top portion of FIG. 46, the side channel suppressionratio is approximately 24 dB.

In order to maximize the resonance power in a selected wavelengthchannel, it is sufficient to adjust the phase shift which is generatedwhen light is being propagated along the third optical waveguide whichis an optical resonator medium. Namely, it is sufficient to adjust theeffective refractive index of the third optical waveguide. In the graphshown in the top portion of FIG. 46, the phase shift is 0.477π.

Hereinafter, the procedure to design the first optical waveguide whichis formed by the first reflection mirror will be described.

The method used to design the first reflection mirror in the presentexample comprises the following steps [1] to [4].

[1] The dimensions (win/wout) of the cross-sectional structure of theoptical waveguide core are specified, and the field distribution of theintrinsic mode of the TE-type polarization and TM-type polarization inthe cross-section are calculated. These dimensions are then adjustedsuch that the effective refractive indices in the two polarizations areequal. w_(in)/w_(out) are then decided such that polarization dependenceis cancelled out in different effective refractive indices.Correspondence relationships between the effective refractive indicesand w_(in)/w_(out) are then obtained so that it is possible to decidethe dimensions of the cross-sectional structure of the optical waveguidecore from the effective refractive indices. This step becomes the designprocess for the cross-sectional structure of the optical waveguide.

[2] The reflection characteristics desired for the reflection mirror arespecified, and the necessary data required to determine the structure ofthe optical waveguide is obtained. What are specified as the reflectioncharacteristics are the reflectance and phase in each wavelength. All ofthe frequency regions that include the desired reflectioncharacteristics from the point of origin (i.e., from a frequency of 0Hz) are included in the frequency range.

[3] The optical waveguide length is provided, and the shape distributionof the effective refractive index extending in the waveguide directionof the optical waveguide is derived from the complex field reflectancespectrum obtained in Step [2] using an inverse scattering problemsolution. This step includes a calculation process to convert thecomplex field reflectance spectrum into a time response, and this is areal number type of conversion.

Steps [2] and [3] become the Bragg grating pattern design process.

[4] Based on the correspondence relationships between the effectiverefractive indices and the cross-sectional dimensions of the opticalwaveguide core obtained in Step [1], the shape extending in the opticalwaveguide direction of the Bragg grating optical waveguide is decidedfrom the shape distribution of the effective refractive index obtainedin Step [3]. This step becomes the reflection mirror design process.

Note that in the same way as in the above described wavelengthdispersion compensation element design step, the order of these stepscan also be switched.

Hereinafter, each step of designing the first reflection mirror will bedescribed in detail.

Step [1]

The cross-sectional structure of the waveguide is the same as that shownin FIG. 5.

If the effective refractive index of the TE polarization is regarded asthe effective refractive index of the waveguide, then the graph shown inFIG. 7 is obtained when relationships between the effective refractiveindex and w_(in) and w_(out) are calculated and plotted.

Step [2]

Using the desired phase characteristics and the power reflectionspectrum in the graph shown in the bottom portion of FIG. 45, thecomplex field reflectance spectrum R (v) of the grating opticalwaveguide was calculated. In an orthogonal coordinate system, R (v) isformed by a real number component and an imaginary number component,however, converting the coordinates into a polar coordinate system andsplitting the complex field reflectance into a phase and absolute valueof the field reflectance simplifies dealing with the reflection mirrorcharacteristics. Therefore, as in the above mentioned Formula A, thecomplex field reflectance is expressed using a polar coordinate system.

The absolute value of the reflectance is normalized as 1 (namely 100%).Within the reflection band of each channel, the absolute value of thefield reflectance is set to 0.95 (i.e. 95%) such that the powerreflectance |R (v)|² becomes 0.9 (90%).

In the reflection mirror of the present example, the wavelengthdispersion in the reflection band of each channel is set to zero. If thewavelength dispersion is zero, the phase forms a linear functionrelative to the frequency. As a result of the above, the opticalcharacteristics specified for the reflection mirror of the presentexample are shown in FIG. 28. In FIG. 28, the left vertical axis showsthe absolute value of the field reflectance |R (v)|, the right verticalaxis shows the phase φ (v), and these are plotted respectively by asolid line and a broken line. The horizontal axis shows the frequency vin units of THz, and specifies optical characteristics by dividing thefrequency from 192.6 THz to 193.6 THz into ten equal channels atintervals of 0.1 THz. The center frequency is 193.1 THz. If this isconverted into a center wavelength, it becomes 1552.52 nm. The spectrumwidth of the reflection band in each channel is 0.01 THz, and it can beseen that the phase changes linearly within this range.

If the spectrum shape of the rectangular reflection band of eachchannel, such as those shown in FIG. 28, is converted into a timewaveform using an inverse Fourier transform, a sinc function type ofimpulse waveform is obtained. If the width of the spectrum of thereflection band is taken as Δv, then the main peak of the sinc functiontype impulse waveform is contained within a time region of approximatelyΔt=3/(Δv). Accordingly, in an optical waveguide that generates areflection band in each channel shown in FIG. 28, the propagation timethat is required between when light is incident and when it is reflectedmust be approximately Δt or even greater than this. The phases, whichchange linearly within the frequency region of each reflection bandshown in FIG. 28, reflect phase delays which are caused by thispropagation time.

In FIG. 28, only the frequency bands in the vicinity of channels where areflection band is present are displayed. All of the frequency bands inwhich a reflection channel is present from the point of origin (i.e.,from 0 THz) are included as desired optical characteristics in theoptical characteristics being target of an inverse scattering method.However, because no reflection channels are present in frequency regionsoutside those shown in FIG. 28, the value of the field reflectance iszero.

Step [3]

The effective refractive index distribution in the waveguide directionof the optical waveguide forming a reflection mirror is derived based onthe inverse scattering problem solution. This procedure is described inStep [3] in the design direction of the above described wavelengthdispersion compensation element.

When specifying the entire length of the optical waveguide, the opticalpath length in accordance with Δt in Step [2] is taken as the minimumvalue, and the specification is made based on the loss and allowabledimensions of the optical waveguide. After the optical waveguide lengthhas been specified, the potential q (z) is determined using an inversescattering problem solution. q (z) is assigned to the above describedFormula 10, and the effective refractive index distribution n_(eff) (z)is obtained. Here, the conversion which is used when an impulse responseis derived from the complex reflectance spectrum R (v) is a real numbertype.

As a result of this, the q (z) which is obtained from the abovedescribed Formula 15 is also a real number, and an effective refractiveindex distribution for an amplitude modulation type Bragg grating inwhich the amplitude of the Bragg grating changes and the phase changesincidentally to the amplitude is obtained. A definition of amplitudemodulation in the present invention is given below.

n_(eff) (z) is plotted in FIG. 29 and FIG. 30. The horizontal axis zshows coordinates in the optical waveguide direction. z=0 mm is thestarting end of the Bragg grating optical waveguide, and z=33.0605 mm isthe finishing end thereof. n_(av) which corresponds to the average valueof the refractive index distribution of the grating optical waveguide is2.348 in the present example.

FIG. 30 shows an enlargement of the effective refractive indexdistribution shown in FIG. 29 for a portion of the optical waveguide. Itcan be seen that n_(eff) oscillates at a cycle of half the valueobtained by dividing the center wavelength (1552.52 nm), whichcorresponds to the center frequency (193.1 THz), by n_(av), so as toexhibit a pattern that regulates the Bragg grating.

One of the features of the amplitude modulation type Bragg grating ofthe present invention is that, as was described in [Example 1 of anoptical filter], the coding of the gradient of the envelope curve of theamplitude of the Bragg grating is inverted.

Step [4]

Based on a correspondence relationship between the effective refractiveindex n_(eff) and the dimensions w_(in) and w_(out) of the opticalwaveguide prepared in Step [1], the effective refractive indexdistribution n_(eff) (z) obtained in Step [3] was converted intodistribution data (i.e., a profile) for w_(in) and w_(out). When theeffective refractive index was determined by using the correspondencerelationship shown in FIG. 6A and FIG. 6B, w_(out) and w_(in), which arethe dimensional parameters to be decided, were determined. As is shownin FIG. 30, the Bragg grating pattern in the effective refractive indexdistribution has a sinusoidal shape.

In a pattern transfer process which is based on dry-etching andlithography using an optical mask, if a rectangular wave type of shapeis employed in which a combination of spaces whose lines, which have afixed width, and widths change in accordance with the pitch arerepeatedly arrayed, there are few fluctuations in the shape after thedry etching. Therefore, after profile data for the optical waveguidedimensions w_(out) and w_(in) has been obtained from the profile of theeffective refractive index, it is converted into a rectangular waveshaped profile. However, in this conversion to a rectangular wave shape,the following two restrictions must be observed.

(1) In the present example, the line width is fixed at 140 nm. Incontrast, the spaces change in accordance with the pitch of the grating.A larger value than the threshold value of the machining accuracy is setfor the line width.

(2) The line amplitude of the rectangular wave shape is adjusted so asto match the core area covered by the sinusoidal Bragg grating pattern.

In accordance with the above flow, the profiles of w_(out) and w_(in)shown in FIG. 31 are obtained. The range of the horizontal axis in FIG.31 is in the same region as the horizontal axis in FIG. 30. FIG. 29through FIG. 31 which were described in the present example are the sameas those described in Example 1 of an optical filter described above.

A design procedure for the first optical waveguide which forms the firstreflection mirror has been described above. However, the second opticalwaveguide which forms the second reflection mirror can also be designedin the same way based on the predetermined phase characteristics and thepower reflection spectrum shown in the graph in the bottom portion ofFIG. 45.

The third optical waveguide is connected in series between the firstoptical waveguide and the second optical waveguide. The length of thethird optical waveguide is as described above. If an optical waveguideon a substrate is used, then an optical waveguide in which the firstoptical waveguide, the third optical waveguide, and the second opticalwaveguide are connected in series can be defined on an optical mask.

The optical resonator of the present example can be used in applicationssuch as optical filters that extract a specific frequency component, andlaser resonators. If it is used for laser resonators, it is necessaryfor the third optical waveguide to have an optical amplificationfunction which utilizes optical gain. By reducing polarizationdependence, it is possible to manufacture an optical resonator thatcorresponds to an arbitrary polarization.

[Amplitude Modulation-Type Bragg Gratings]

In the above description, it was described that an amplitudemodulation-type Bragg grating based on exemplary embodiments differsfrom a chirped Bragg grating. In contrast, according to the samplingtheorem described below, a Bragg grating pattern is defined as having asingle meaning (i.e., as being unique), and differences such asamplitude modulation types or chirped types of Bragg grating pattern didnot appear. However, this applies to continuous effective refractiveindex distributions, and does not apply to discrete effective refractiveindex distributions that have undergone coarse graining. This point issupplemented below.

The effective refractive index distribution of a Bragg grating isobtained as an effective refractive index distribution for discretepoints sampled at fixed intervals on a coordinate axis which extends inthe light propagation direction. If the sampling theorem derived byNyquist, Shannon, and Someya is applied to the effective refractiveindex distribution of a Bragg grating, then if the coordinate interval,namely, the sampling cycle of discrete points in the effectiverefractive index distribution obtained from a design is set to not morethan half the local cycle (i.e., the pitch) of the sinusoidal changes inthe effective refractive index of the targeted Bragg grating, then thecontinuous effective refractive index distribution which corresponds tothe discrete effective refractive index distribution is determined asbeing unique. In order to determine a continuous effective refractiveindex distribution, as is shown in the following Formula B, aWhittaker-Shannon interpolation formula which utilizes a sinc functionis used.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 18} \right\rbrack & \; \\{{q(z)} = {\sum\limits_{n = {- \infty}}^{+ \infty}\left\{ {{{q\left( {nZ}_{IS} \right)} \cdot \sin}\;{c\left\lbrack {\pi\left( {\frac{z}{Z_{IS}} - n} \right)} \right\rbrack}} \right\}}} & \left( {{Formula}\mspace{14mu} B} \right)\end{matrix}$

Here, z is the continuous coordinates, q (z) expresses a potential thatprovides an effective refractive index distribution defined bycontinuous coordinates, q (nZ_(IS)) expresses a potential that providesan effective refractive index defined by discrete coordinates, andZ_(IS) is the sampling cycle. In the present example, because thesampling cycle is ⅕^(th) the pitch, the effective refractive index isdecided uniquely. n is an integer specifying a discrete coordinatepoint. In reality, because the Bragg grating length is finite, n isfinite. Reproducing the (original) continuous waveform from the discretewaveform is called “reconstruction”. In order to achieve a Bragg gratinghaving predetermined optical characteristics, it is necessary for theeffective refractive index distribution to be able to be reconstructeduniquely. The above Formula 10 is used to obtain the effectiverefractive index n_(eff) from the potential.

It should be noted that, in order to form a Bragg grating pattern byoptical exposure, it is necessary to prepare data of a Bragg gratingpattern for an optical mask. The pattern data for an optical mask isprepared as a digital file in GDS format or the like. Because the numberof data items is unlimited in a continuous effective refractive indexdistribution, the file capacity is infinite. Accordingly, it isnecessary to use a discrete effective refractive index distributionwhich has a limited number of data items as the optical mask patterndata. As a result of this, even if a continuous effective refractiveindex distribution is reconstructed, it is necessary to convert it to adiscrete distribution. Because of this, the discrete effectiverefractive index distribution before the reconstruction is used for themask pattern data. In a discrete effective refractive indexdistribution, the shape of the effective refractive index distributiondiffers depending on the discretized sampling cycle and the mode ofdiscretization. This fact generates the differences between amplitudemodulation-type and chirped Bragg gratings. If there is a need tofurther improve the accuracy with which predetermined opticalcharacteristics are reproduced, then it is possible to use an effectiverefractive index distribution which has been discretized afterundergoing reconstruction as the mask data.

For example, if a case in which optical characteristics such as thoseshown in FIG. 47 are specified as the predetermined characteristics areconsidered. In FIG. 47, an example of the characteristics of an opticalelement having a single reflection channel is shown. In the top portionof the graph in FIG. 47, the frequency dependence of the delay time isplotted, while in the bottom portion of the graph in FIG. 47, theabsolute value of the complex field reflectance and phase are plotted.The frequency width of the reflection channel is 1.244 THz. The centerfrequency is 193.1 THz. The spectrum occupancy of the half value of thewidth of the reflection channel is approximately 0.32% of the centerfrequency, which is a narrow band. Note that in each example of thepresent invention, the width of each channel is even narrower.

If a Bragg grating that provides the above characteristics is formed bya chirped Bragg grating, then a resolution that corresponds to changingthe pitch by a maximum of only 0.32% is sought for the discretization ofthe coordinate axis of the Bragg grating. Namely, the number of segmentsused to discretize each pitch is at least 313 which is an inverse numberof 0.32%. In order to reproduce the fact that the pitch changescontinuously in the light waveguide direction, it is necessary to raisethe resolution even further, so that the number of data items increaseseven further. Accordingly, if an attempt to accurately construct achirped Bragg grating is made, the number of data items is enormous, andthe processing itself of the mask data becomes difficult. Moreover, amaximum amount of change in the pitch of only 0.32% is onlyapproximately 1 nm if the pitch center value is taken as 340 nm. Inorder to chirp this, it is necessary to miniaturize this even further,however, it is difficult to accurately manufacture an optical maskpattern at a sub-nanometer accuracy level.

Accordingly, it can be said that an amplitude modulation-type Bragggrating is advantageous from the standpoints of improving the accuracyof the manufacturing process, and of both reducing processing time andcosts. As has been described above, in order to select an amplitudemodulation-type Bragg grating pattern, it is sufficient to performcoarse graining in which the discretized resolution of the coordinateaxis is taken as more than an amount of change in the pitch whichcorresponds to the half value of the width of the reflection band, inother words, the discretized resolution of the coordinate axis is takenas more than (not less than) the maximum value of the amount of changefrom the pitch center value in a chirped Bragg grating. As a result ofthis, the continuous changes in pitch in a chirped Bragg grating areaccumulated, and the feature is evident that the coding of the gradientof the envelope curve of the amplitude of the Bragg grating is invertedat a single isolated coordinate point, and that the phase changescontinuously incidentally to this.

EXAMPLES

Hereinafter, exemplary embodiments will be described in greater detailusing comparisons between Examples and Comparative examples.

In order to evaluate the effects of roughness on the core side walls,the basic propagation mode was simulated using a mode solver, and theeffective refractive index of the ribs was calculated. In Examples 1 and2, the optical confinement coefficient in the core region was alsocalculated.

Simulation Example 1

In Example 1, in the planar optical waveguide element of the firstembodiment shown in FIGS. 1A and 1B, the top cladding 7, bottom cladding6, and center gap 3 were formed from SiO₂ having a refractive index of1.45, and the high refractive index ribs 1 and 2 were formed from Sihaving a refractive index of 3.48. The dimensions of the respectiveportions were set as height t₁ of the rectangular parallelepipedportions 1 b and 2 b=250 nm, thickness t₂ of the planar portions 1 a and1 b=50 nm, width w1 of the rectangular parallelepiped portions 1 b and 2b=280 nm, and width w2 of the center gap 3=160 nm.

FIG. 48 shows the light intensity distribution of the core expressed asa contour diagram as a simulation result for Example 1. Note that, inFIG. 48, the interfaces of each material are also shown for a reference.These results were as follows: the effective refractive index of thebasic propagation mode for w₁=280 nm was 2.1640. Moreover, the opticalconfinement coefficient in rib areas in two locations of the highrefractive index ribs 1 and 2 which each had cross-sectional areas ofwidth w₁×height (t₁+t₂) was 70.5%, and it was found that the propagatedlight was mainly confined in the silicon core area.

Furthermore, in order to evaluate the effects of core (rib) side wallroughness generated in an etching process during manufacturing, w₁ alonewas altered to 275 nm and 285 nm, and the effective refractive index ofthe basic propagation mode was measured in the same type of simulation.It was found that the measured effective refractive indices were 2.1458and 2.1827 respectively. Namely, the effective refractive index varied−0.84% relative to a variation of −1.79% in w₁, and the effectiverefractive index varied +0.86% relative to a variation of +1.79% in w₁.

Simulation Example 2

In Example 2, in the planar optical waveguide element of the secondembodiment shown in FIG. 2, the top cladding 7A, bottom cladding 6A, andcenter gap 3A were formed from SiO₂ having a refractive index of 1.45,and the high refractive index cores 1A and 2A were formed from siliconnitride having a refractive index of 2.0. The dimensions of therespective portions were set as height t₃ of the cores 1A and 2A and ofthe center gap 3A=600 nm, width w₃ (on one side) of the cores 1A and2A=340 nm, and width w₄ of the center gap 3A=160 nm.

FIG. 49 shows the light intensity distribution of the core expressed asa contour diagram as a simulation result for Example 2. Note that, inFIG. 49, the interfaces of each material are also shown for a reference.These results were as follows: the effective refractive index of thebasic propagation mode for w₃=340 nm was 1.5690. Moreover, the opticalconfinement coefficient in the silicon nitride core areas in twolocations each having cross-sectional areas of width w₃×height t₃ was41.2%. In contrast to this, the optical confinement coefficient in thecenter gap area having a cross-sectional area of width w₄×height t₃ was22.1%, and it was found that the propagated light was mainly confined inthe silicon nitride core area.

Furthermore, in order to evaluate the effects of core side wallroughness generated in an etching process during manufacturing, w₁ alonewas altered to 335 nm and 345 nm, and the effective refractive index ofthe basic propagation mode was measured in the same type of simulation.It was found that the measured effective refractive indices were 1.5663and 1.5717 respectively. Namely, the effective refractive index varied−0.17% relative to a variation of −1.47% in w₁, and the effectiverefractive index varied +0.17% relative to a variation of +1.47% in w₁.

Simulation Comparative Example 1

In Comparative example 1, in the planar optical waveguide element havingno center gap as shown in FIGS. 50A and 50B, the top cladding 207 andthe bottom cladding 206 were formed from SiO₂ having a refractive indexof 1.45, and the high refractive index ribs 201 and 202 were formed fromSi having a refractive index of 3.48. The dimensions of the respectiveportions were set as height t₁ of the rectangular parallelepipedportions 201 b and 202 b=250 nm, thickness t₂ of the planar portions 201a and 201 b=50 nm, and width 2 w ₁ of the ribs=380 nm (corresponding to190 nm of w₁ on one side). The materials used for each portion, as wellas t₁ and t₂ were the same as in the above-described Example 1. w1 was avalue determined as a condition for single mode propagation.

FIG. 52 shows the light intensity distribution of the core expressed asa contour diagram as a simulation result for Comparative example 1. Notethat, in FIG. 52, the interfaces of each material are also shown for areference. These results were as follows: the effective refractive indexof the basic propagation mode for 2 w ₁=380 nm was 2.4905. Moreover, inorder to evaluate the effects of core (rib) side wall roughnessgenerated in an etching process during manufacturing, 2 w ₁ alone wasaltered to 370 nm and 390 nm, and the effective refractive index of thebasic propagation mode was measured in the same type of simulation. Itwas found that the measured effective refractive indices were 2.4657 and2.5149 respectively. Namely, the effective refractive index varied −1.0%relative to a variation of −2.6% in 2 w ₁, and the effective refractiveindex varied +0.98% relative to a variation of +2.6% in 2 w ₁.

Simulation Comparative Example 2

In Comparative example 2, in the planar optical waveguide element havingno center gap as shown in FIG. 51, the top cladding 307 and the bottomcladding 306 were formed from SiO₂ having a refractive index of 1.45,and the high refractive index core 301 was formed from silicon nitridehaving a refractive index of 2.0. The dimensions of the respectiveportions were set as height of the core 301=600 nm, width of the core301=680 nm (corresponding to 2 w ₃ of Example 2). The materials used foreach portion, as well as the cross-sectional dimensions of the core werethe same as in the above-described Example 2.

FIG. 53 shows the light intensity distribution of the core expressed asa contour diagram as a simulation result for Comparative example 2. Notethat, in FIG. 53, the interfaces of each material are also shown for areference. These results were as follows: the effective refractive indexof the basic propagation mode for a core width of 680 nm was 1.6482.Moreover, in order to evaluate the effects of core side wall roughnessgenerated in an etching process during manufacturing, the core widthalone was altered to 670 nm and 690 nm, and the effective refractiveindex of the basic propagation mode was measured in the same type ofsimulation. It was found that the measured effective refractive indiceswere 1.6446 and 1.6517 respectively. Namely, the effective refractiveindex varied −0.22% relative to a variation of −1.47% in core width, andthe effective refractive index varied +0.21% relative to a variation of+1.47% in core width.

Simulation Comparative Example 3

The basic propagation mode was simulated using a mode solver in the sameway as in the above-described Examples 1 and 2 and Comparative examples1 and 2 for the structure described in FIGS. 1 (a) and (b) and FIG. 3(a) of the above-described Non-patent document 4. The results of thisshowed that the optical confinement coefficient in a rectangular siliconcore area (having a refractive index of 3.48, and width 180 nm×height300 nm×two locations) was 42.7%. Moreover, the optical confinementcoefficient in silica glass of the center gap area (having a refractiveindex of 1.46, and width 50 nm×height 300 nm) was 48.0%. From this itwas found that the propagated light was mainly confined in the centergap area (i.e., the slot area).

Comparison Between Examples and Comparative Examples

By comparing Example 1 with Comparative example 1, and Example 2 withComparative example 2, it was found that, in each example in which acenter gap was provided, variations in the effective refractive index ofthe basic propagation mode relative to variations in the core width weresmaller. Namely, according to the present examples, it is possible toreduce the effects of core side wall roughness.

Moreover, by comparing Examples 1 and 2 with Comparative example 3, thedifference was found that, while in Comparative example 3 propagatedlight was mainly confined within the center gap area, in the Examplespropagated light was mainly confined within high refractive index core.This difference shows a unique structure in which, by narrowing thecenter gap in Comparative example 3, propagated light is confined withinthe center gap area which has a low refractive index.

Exemplary embodiments described herein enable propagated light to beconfined mainly within the high refractive index core, unlike the casesof Non-patent document 4 and Comparative example 3. Because of this,side wall roughness in the high refractive index core has an effect onoptical characteristics. In contrast to this, by dividing the highrefractive index core into two areas, and providing a low refractiveindex gap area between these two areas, the effects of side wallroughness in the high refractive index core are inhibited.

INDUSTRIAL APPLICABILITY

According to exemplary embodiments described herein, it is possible toprovide a planar optical waveguide element that makes it possible toreduce the effects of core side wall roughness which is inevitablygenerated in a manufacturing process, and also possible to provide awavelength dispersion compensation element and to a design methodthereof which uses this planar optical waveguide element.

Although a few exemplary embodiments have been shown and described, itwould be appreciated by those skilled in the art that changes may bemade in these embodiments without departing from the principles andspirit of the inventive concept, the scope of which is defined in theclaims and their equivalents.

What is claimed is:
 1. A planar optical waveguide element comprising: acore of an optical waveguide comprising a first portion and a secondportion, extending in a propagation direction of guided light, and a gapportion disposed between the first portion and the second portion in awidth direction of the core, perpendicular to the propagation directionof guided light; and a first Bragg grating pattern and a second Bragggrating pattern provided on the core, wherein the gap portion has arefractive index lower than a refractive index of the first portion andthe second portion of the core; wherein a single mode is propagated inthe optical waveguide so as to span across the first portion and thesecond portion of the core; wherein the first Bragg grating pattern andthe second Bragg grating pattern are mutually parallel and extend in thepropagation direction of guided light; wherein the first Bragg gratingpattern comprises recessed and protruding portions that are formed onboth outer side walls of the core along the propagation direction ofguided light; wherein the second Bragg grating pattern comprisesrecessed and protruding portions that are formed, along the propagationdirection of guided light, on both inner side walls of a groove that isformed on a top portion of the core at a center of the core in the widthdirection; and wherein the protruding portions of the first Bragggrating pattern where a core width is wide correspond with theprotruding portions of the second Bragg grating pattern where a width ofthe groove is narrow, and the recessed portions of the first Bragggrating pattern where the core width is narrow correspond with therecessed portions of the second Bragg grating pattern where the width ofthe groove is wide.
 2. The planar optical waveguide element according toclaim 1, wherein the first Bragg grating pattern and the second Bragggrating pattern comprise a plurality of isolated single coordinatepoints where a sign of a gradient of an envelope curve of an amplitudeof a Bragg grating is inverted.